Solve the Equation: (2x²-32)/8 = (x+4)/2 Step-by-Step

2x2−328=x+42 \frac{2x^2-32}{8}=\frac{x+4}{2}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:04 Take out 2 from the parentheses
00:21 Divide 8 by 2
00:28 Use the shortened multiplication formulas
00:43 Convert from 16 to 4 squared
00:56 Again use the shortened multiplication formulas
01:05 Multiply by 4 to eliminate the fraction
01:29 Reduce what we can
01:55 Isolate X
02:05 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

2x2−328=x+42 \frac{2x^2-32}{8}=\frac{x+4}{2}

2

Step-by-step solution

To solve the equation 2x2−328=x+42 \frac{2x^2-32}{8} = \frac{x+4}{2} , let's proceed through these steps:

  • Step 1: Simplify and eliminate fractions by cross-multiplying.
  • Step 2: Rearrange and simplify the resulting equation.
  • Step 3: Solve for the variable x x .

Now, let's work through each step:

Step 1: Cross-multiply to eliminate the fractions.
We perform cross multiplication as follows:

(2x2−32)×2=8×(x+4)\left(2x^2 - 32\right) \times 2 = 8 \times (x + 4)

This gives us:

4x2−64=8x+324x^2 - 64 = 8x + 32

Step 2: Rearrange and simplify the equation.
Move all terms to one side to set the equation to zero:

4x2−8x−96=04x^2 - 8x - 96 = 0

Simplify by dividing the entire equation by 4:

x2−2x−24=0x^2 - 2x - 24 = 0

Step 3: Solve the quadratic equation by factoring.
Factor the quadratic equation:

(x−6)(x+4)=0(x - 6)(x + 4) = 0

Set each factor to zero and solve for x x :

  • x−6=0⇒x=6x - 6 = 0 \Rightarrow x = 6
  • x+4=0⇒x=−4x + 4 = 0 \Rightarrow x = -4

Considering the given multiple-choice answers, the correct solution is:

x=6 x = 6

Therefore, the solution to the problem is x=6 x = 6 .

3

Final Answer

6

Practice Quiz

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Solve:

\( (2+x)(2-x)=0 \)

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