Solve the Equation: (x+2)(2x-4) = 2x²+x+10

Q: Why did the $ x^2 $ terms disappear?

Great observation! When you have identical terms on both sides like $ 2x^2 $, they cancel out when you subtract. This turns our quadratic equation into a simple linear equation!

Q: How do I expand $ (x+2)(2x-4) $ without making mistakes?

Use FOIL method: First × First, Outer × Outer, Inner × Inner, Last × Last.$ x \times 2x = 2x^2 $$ x \times (-4) = -4x $$ 2 \times 2x = 4x $$ 2 \times (-4) = -8 $Then combine: $ 2x^2 - 4x + 4x - 8 = 2x^2 - 8 $

Q: What if I get a different equation type after simplifying?

That's normal! Sometimes quadratic equations simplify to linear equations (like this one) or even to contradictions. Always follow the algebra wherever it leads you.

Q: Should I always move everything to one side?

Yes! Setting the equation equal to zero is the standard approach. It makes it easier to see what you're solving and helps avoid sign errors.

Q: How can I check if $ x = -18 $ is really correct?

Substitute back into the original equation:Left side: $ (-18+2)(2(-18)-4) = (-16)(-40) = 640 $Right side: $ 2(-18)^2 + (-18) + 10 = 648 - 18 + 10 = 640 $Since both sides equal 640, our answer is correct!

Quadratic Equations with Like Term Elimination

$(x+2)(2x-4)=2x^2+x+10$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Open parentheses properly multiply each factor by each factor

00:31 Collect terms

00:41 Reduce what we can

00:55 Isolate the unknown X

01:04 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$(x+2)(2x-4)=2x^2+x+10$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Expand the left-hand side of the equation.
Step 2: Set the equation to standard quadratic form.
Step 3: Factor the quadratic equation.
Step 4: Solve for $x$ .

Let's proceed through each step:

Step 1: Expand the left-hand side using the distributive property:

$(x+2)(2x-4) = x(2x) + x(-4) + 2(2x) + 2(-4)$

$= 2x^2 - 4x + 4x - 8$

$= 2x^2 - 8$

Step 2: Set the equation to quadratic form:

Set the expanded result equal to the right-hand side:

$2x^2 - 8 = 2x^2 + x + 10$

Step 3: Subtract the right-hand side from the left:

$2x^2 - 8 - (2x^2 + x + 10) = 0$

Simplify:

$2x^2 - 8 - 2x^2 - x - 10 = 0$

$-x - 18 = 0$

Step 4: Solve for $x$ :

$-x = 18$

Divide by -1:

$x = -18$

Therefore, the solution to the problem is $x = -18$ .

Checking against the given choices, choice 1 matches: $-18$ .

Final Answer

$-18$

Key Points to Remember

Essential concepts to master this topic

Expansion: Use distributive property to expand both sides completely
Technique: Subtract matching terms: $2x^2 - 2x^2 = 0$
Check: Substitute $x = -18$ back into original equation ✓

Common Mistakes

Avoid these frequent errors

Incorrectly expanding the left side
Don't forget the middle terms when expanding $(x+2)(2x-4)$ = wrong coefficients! Students often get $2x^2 - 8$ instead of $2x^2 - 4x + 4x - 8$ . Always use FOIL or distributive property systematically for all four terms.

Practice Quiz

Test your knowledge with interactive questions

$$ x+7=14 $$

$x=\text{?}$

FAQ

Everything you need to know about this question

Why did the $x^2$ terms disappear?

Great observation! When you have identical terms on both sides like $2x^2$ , they cancel out when you subtract. This turns our quadratic equation into a simple linear equation!

How do I expand $(x+2)(2x-4)$ without making mistakes?

Use FOIL method: First × First, Outer × Outer, Inner × Inner, Last × Last.
$x \times 2x = 2x^2$
$x \times (-4) = -4x$
$2 \times 2x = 4x$
$2 \times (-4) = -8$
Then combine: $2x^2 - 4x + 4x - 8 = 2x^2 - 8$

What if I get a different equation type after simplifying?

That's normal! Sometimes quadratic equations simplify to linear equations (like this one) or even to contradictions. Always follow the algebra wherever it leads you.

Should I always move everything to one side?

Yes! Setting the equation equal to zero is the standard approach. It makes it easier to see what you're solving and helps avoid sign errors.

How can I check if $x = -18$ is really correct?

Substitute back into the original equation:
Left side: $(-18+2)(2(-18)-4) = (-16)(-40) = 640$
Right side: $2(-18)^2 + (-18) + 10 = 648 - 18 + 10 = 640$
Since both sides equal 640, our answer is correct!

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Solve the Equation: (x+2)(2x-4) = 2x²+x+10

Quadratic Equations with Like Term Elimination

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why did the $x^2$ terms disappear?

How do I expand $(x+2)(2x-4)$ without making mistakes?

What if I get a different equation type after simplifying?

Should I always move everything to one side?

How can I check if $x = -18$ is really correct?

🌟 Unlock Your Math Potential

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Solve the Equation: (x+2)(2x-4) = 2x²+x+10

Quadratic Equations with Like Term Elimination

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why did the x2 x^2 x2 terms disappear?

How do I expand (x+2)(2x−4) (x+2)(2x-4) (x+2)(2x−4) without making mistakes?

What if I get a different equation type after simplifying?

Should I always move everything to one side?

How can I check if x=−18 x = -18 x=−18 is really correct?

🌟 Unlock Your Math Potential

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Why did the $x^2$ terms disappear?

How do I expand $(x+2)(2x-4)$ without making mistakes?

How can I check if $x = -18$ is really correct?