Solve 2x^2+7=101

$$2 x ^ { 2 } + 7 = 101$$

Solve for x

$$x=\sqrt{47}\approx 6.8556546$$

$$x=-\sqrt{47}\approx -6.8556546$$

Steps by Finding Square Root

Subtract 7 from both sides.

$$2x^{2}=101-7$$

Subtract 7 from 101 to get 94.

$$2x^{2}=94$$

Divide both sides by 2.

$$x^{2}=\frac{94}{2}$$

Divide 94 by 2 to get 47.

$$x^{2}=47$$

Take the square root of both sides of the equation.

$$x=\sqrt{47} x=-\sqrt{47}$$

Steps Using the Quadratic Formula

Subtract 101 from both sides.

$$2x^{2}+7-101=0$$

Subtract 101 from 7 to get -94.

$$2x^{2}-94=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -94 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-94\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-94\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-94\right)}}{2\times 2}$$

Multiply -8 times -94.

$$x=\frac{0±\sqrt{752}}{2\times 2}$$

Take the square root of 752.

$$x=\frac{0±4\sqrt{47}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±4\sqrt{47}}{4}$$

Now solve the equation x=\frac{0±4\sqrt{47}}{4} when ± is plus.

$$x=\sqrt{47}$$

Now solve the equation x=\frac{0±4\sqrt{47}}{4} when ± is minus.

$$x=-\sqrt{47}$$

The equation is now solved.

$$x=\sqrt{47} x=-\sqrt{47}$$