Solve 2x^2-58=70

$$2 x ^ { 2 } - 58 = 70$$

Solve for x

$$x=8$$

$$x=-8$$

Steps Using Difference of Squares

Subtract 70 from both sides.

$$2x^{2}-58-70=0$$

Subtract 70 from -58 to get -128.

$$2x^{2}-128=0$$

Divide both sides by 2.

$$x^{2}-64=0$$

Consider x^{2}-64. Rewrite x^{2}-64 as x^{2}-8^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-8\right)\left(x+8\right)=0$$

To find equation solutions, solve x-8=0 and x+8=0.

$$x=8 x=-8$$

Steps by Finding Square Root

Add 58 to both sides.

$$2x^{2}=70+58$$

Add 70 and 58 to get 128.

$$2x^{2}=128$$

Divide both sides by 2.

$$x^{2}=\frac{128}{2}$$

Divide 128 by 2 to get 64.

$$x^{2}=64$$

Take the square root of both sides of the equation.

$$x=8 x=-8$$

Steps Using the Quadratic Formula

Subtract 70 from both sides.

$$2x^{2}-58-70=0$$

Subtract 70 from -58 to get -128.

$$2x^{2}-128=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -128 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-128\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-128\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-128\right)}}{2\times 2}$$

Multiply -8 times -128.

$$x=\frac{0±\sqrt{1024}}{2\times 2}$$

Take the square root of 1024.

$$x=\frac{0±32}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±32}{4}$$

Now solve the equation x=\frac{0±32}{4} when ± is plus. Divide 32 by 4.

$$x=8$$

Now solve the equation x=\frac{0±32}{4} when ± is minus. Divide -32 by 4.

$$x=-8$$

The equation is now solved.

$$x=8 x=-8$$