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

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

Solve for x

$$x = \frac{\sqrt{30}}{2} \approx 2.738612788$$

$$x = -\frac{\sqrt{30}}{2} \approx -2.738612788$$

Steps by Finding Square Root

Multiply both sides of the equation by 2.

$$2x^{2}+10=5^{2}$$

Calculate 5 to the power of 2 and get 25.

$$2x^{2}+10=25$$

Subtract 10 from both sides.

$$2x^{2}=25-10$$

Subtract 10 from 25 to get 15.

$$2x^{2}=15$$

Divide both sides by 2.

$$x^{2}=\frac{15}{2}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{30}}{2} x=-\frac{\sqrt{30}}{2}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 2.

$$2x^{2}+10=5^{2}$$

Calculate 5 to the power of 2 and get 25.

$$2x^{2}+10=25$$

Subtract 25 from both sides.

$$2x^{2}+10-25=0$$

Subtract 25 from 10 to get -15.

$$2x^{2}-15=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -15 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-15\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-15\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-15\right)}}{2\times 2}$$

Multiply -8 times -15.

$$x=\frac{0±\sqrt{120}}{2\times 2}$$

Take the square root of 120.

$$x=\frac{0±2\sqrt{30}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±2\sqrt{30}}{4}$$

Now solve the equation x=\frac{0±2\sqrt{30}}{4} when ± is plus.

$$x=\frac{\sqrt{30}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{30}}{4} when ± is minus.

$$x=-\frac{\sqrt{30}}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{30}}{2} x=-\frac{\sqrt{30}}{2}$$