Solve the Quadratic Equation: x² - 36 = 6x - 36

Q: Why do I need to get everything on one side first?

Factoring only works when one side equals zero! When you have $ x^2 - 6x = 0 $, you can use the zero product property to find solutions.

Q: How do I know when to factor out a common term?

Look for terms that share the same variable. In $ x^2 - 6x = 0 $, both terms have x, so factor out $ x(x - 6) = 0 $.

Q: What is the zero product property?

If $ a \times b = 0 $, then either $ a = 0 $ or $ b = 0 $ (or both). So from $ x(x - 6) = 0 $, we get $ x = 0 $ or $ x - 6 = 0 $.

Q: Can all quadratic equations be solved by factoring?

No! Some quadratics don't factor nicely with integers. If factoring doesn't work, you can use the quadratic formula or completing the square instead.

Q: Why are there two solutions?

Quadratic equations create parabolas when graphed, and this equation asks where the parabola crosses the x-axis. Most parabolas cross twice, giving two solutions.

Q: How do I check if my solutions are correct?

Substitute each solution back into the original equation. For $ x = 0 $: $ 0^2 - 36 = -36 $ and $ 6(0) - 36 = -36 $ ✓

Quadratic Equations with Factoring Method

Solve the following equation:

$x^2-36=6x-36$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find X

00:03 Factor 36 into 6 squared

00:10 Factor 36 into factors 6 and 6

00:18 Take out the common factor from parentheses

00:28 Use the shortened multiplication formulas

00:40 Use the shortened multiplication formulas and build a trinomial

00:45 Divide by the common factor

01:00 Reduce what is possible

01:03 Isolate X

01:16 This is the solution we got

01:20 Check if we divided by 0

01:25 For division by 0, X must equal 6

01:28 Substitute in our equation and solve

01:34 It works out, so this is also a solution to the question

01:40 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

Solve the following equation:

$x^2-36=6x-36$

Step-by-step solution

To solve the equation $x^2 - 36 = 6x - 36$ , follow these steps:

Simplify the equation by subtracting 6x and 36 from both sides to get: $x^2 - 6x = 0$ .
Notice that the equation can be factored as it has a common factor: $x(x - 6) = 0$ .
According to the zero product property, set each factor equal to zero: $x = 0$ or $x - 6 = 0$ .
Solve each resulting equation: $x = 0$ and $x = 6$ .

Therefore, the solutions to the quadratic equation $x^2 - 36 = 6x - 36$ are $x = 0$ or $x = 6$ .

Final Answer

$0~or~6$

Key Points to Remember

Essential concepts to master this topic

Rearrangement: Move all terms to one side to get standard form
Factoring: Find common factor: $x(x - 6) = 0$
Verification: Check both solutions: $0^2 - 36 = 6(0) - 36$ and $6^2 - 36 = 6(6) - 36$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to move all terms to one side first
Don't try to factor $x^2 - 36 = 6x - 36$ directly = confusion and wrong solutions! You need all terms on one side to see the true structure. Always rearrange to get $x^2 - 6x = 0$ first, then factor.

Practice Quiz

Test your knowledge with interactive questions

Solve the following equation:

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

FAQ

Everything you need to know about this question

Why do I need to get everything on one side first?

Factoring only works when one side equals zero! When you have $x^2 - 6x = 0$ , you can use the zero product property to find solutions.

How do I know when to factor out a common term?

Look for terms that share the same variable. In $x^2 - 6x = 0$ , both terms have x, so factor out $x(x - 6) = 0$ .

What is the zero product property?

If $a \times b = 0$ , then either $a = 0$ or $b = 0$ (or both). So from $x(x - 6) = 0$ , we get $x = 0$ or $x - 6 = 0$ .

Can all quadratic equations be solved by factoring?

No! Some quadratics don't factor nicely with integers. If factoring doesn't work, you can use the quadratic formula or completing the square instead.

Why are there two solutions?

Quadratic equations create parabolas when graphed, and this equation asks where the parabola crosses the x-axis. Most parabolas cross twice, giving two solutions.

How do I check if my solutions are correct?

Substitute each solution back into the original equation. For $x = 0$ : $0^2 - 36 = -36$ and $6(0) - 36 = -36$ ✓

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Solve the Quadratic Equation: x² - 36 = 6x - 36

Quadratic Equations with Factoring Method

❤️ 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 do I need to get everything on one side first?

How do I know when to factor out a common term?

What is the zero product property?

Can all quadratic equations be solved by factoring?

Why are there two solutions?

How do I check if my solutions are correct?

🌟 Unlock Your Math Potential

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