Miriam Blair

2023-03-14

How to solve $2{x}^{2}-2=6$?

First, to isolate the ${x}^{2}$ term and maintain the equation's balance, add $2$ to each side of the equation:
$2{x}^{2}-2+2=6+2$
$2{x}^{2}-0=8$
$2{x}^{2}=8$
Next, divide each side of the equation by $2$ to isolate ${x}^{2}$ while keeping the equation balanced:
$\frac{2{x}^{2}}{2}=\frac{8}{2}$
$\frac{\overline{)2}{x}^{2}}{\overline{)2}}=4$
${x}^{2}=4$
To solve for $x$ while keeping the equation balanced, take the square root of each side of the equation. Remember that there are two solutions—one negative and one positive—when computing the square root of a number:
$\sqrt{{x}^{2}}=±\sqrt{4}$
$x=±\sqrt{4}=±2$

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