Solve the Quadratic Equation: 2x² - 8 = x² + 4

Solve the following exercise:

2x2−8=x2+4 2x^2-8=x^2+4

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find X
00:03 Isolate X
00:34 Extract root
00:38 When extracting a root there are always 2 solutions (positive, negative)
00:41 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

Solve the following exercise:

2x2−8=x2+4 2x^2-8=x^2+4

2

Step-by-step solution

First, we move the terms to one side equal to 0.

2x2−x2−8−4=0 2x^2-x^2-8-4=0

We simplify :

x2−12=0 x^2-12=0

We use the shortcut multiplication formula to solve:

x2−(12)2=0 x^2-(\sqrt{12})^2=0

(x−12)(x+12)=0 (x-\sqrt{12})(x+\sqrt{12})=0

x=±12 x=\pm\sqrt{12}

3

Final Answer

±12 ±\sqrt{12}

Practice Quiz

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Solve for X:

\( x\cdot x=49 \)

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