Solve 2x^2=102/-2+5^2

$$2 x ^ { 2 } = 10 \frac { 2 } { - 2 } + 5 ^ { 2 }$$

Solve for x

$$x=\sqrt{17}\approx 4.123105626$$

$$x=-\sqrt{17}\approx -4.123105626$$

Steps by Finding Square Root

Multiply both sides of the equation by -2.

$$-4x^{2}=10\left(-2\right)+2-2\times 5^{2}$$

Multiply 10 and -2 to get -20.

$$-4x^{2}=-20+2-2\times 5^{2}$$

Add -20 and 2 to get -18.

$$-4x^{2}=-18-2\times 5^{2}$$

Calculate 5 to the power of 2 and get 25.

$$-4x^{2}=-18-2\times 25$$

Multiply -2 and 25 to get -50.

$$-4x^{2}=-18-50$$

Subtract 50 from -18 to get -68.

$$-4x^{2}=-68$$

Divide both sides by -4.

$$x^{2}=\frac{-68}{-4}$$

Divide -68 by -4 to get 17.

$$x^{2}=17$$

Take the square root of both sides of the equation.

$$x=\sqrt{17} x=-\sqrt{17}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by -2.

$$-4x^{2}=10\left(-2\right)+2-2\times 5^{2}$$

Multiply 10 and -2 to get -20.

$$-4x^{2}=-20+2-2\times 5^{2}$$

Add -20 and 2 to get -18.

$$-4x^{2}=-18-2\times 5^{2}$$

Calculate 5 to the power of 2 and get 25.

$$-4x^{2}=-18-2\times 25$$

Multiply -2 and 25 to get -50.

$$-4x^{2}=-18-50$$

Subtract 50 from -18 to get -68.

$$-4x^{2}=-68$$

Add 68 to both sides.

$$-4x^{2}+68=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -4 for a, 0 for b, and 68 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-4\right)\times 68}}{2\left(-4\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-4\right)\times 68}}{2\left(-4\right)}$$

Multiply -4 times -4.

$$x=\frac{0±\sqrt{16\times 68}}{2\left(-4\right)}$$

Multiply 16 times 68.

$$x=\frac{0±\sqrt{1088}}{2\left(-4\right)}$$

Take the square root of 1088.

$$x=\frac{0±8\sqrt{17}}{2\left(-4\right)}$$

Multiply 2 times -4.

$$x=\frac{0±8\sqrt{17}}{-8}$$

Now solve the equation x=\frac{0±8\sqrt{17}}{-8} when ± is plus.

$$x=-\sqrt{17}$$

Now solve the equation x=\frac{0±8\sqrt{17}}{-8} when ± is minus.

$$x=\sqrt{17}$$

The equation is now solved.

$$x=-\sqrt{17} x=\sqrt{17}$$