Solve 1/2*x^2=1/2*13.616^2+9.81*18.9

$$\frac { 1 } { 2 } \times x ^ { 2 } = \frac { 1 } { 2 } \times 13.616 ^ { 2 } + 9.81 \times 18.9$$

Solve for x

$$x = \frac{\sqrt{34763341}}{250} \approx 23.584178086$$

$$x = -\frac{\sqrt{34763341}}{250} \approx -23.584178086$$

Steps by Finding Square Root

Calculate 13.616 to the power of 2 and get 185.395456.

$$\frac{1}{2}x^{2}=\frac{1}{2}\times 185.395456+9.81\times 18.9$$

Multiply \frac{1}{2} and 185.395456 to get \frac{1448402}{15625}.

$$\frac{1}{2}x^{2}=\frac{1448402}{15625}+9.81\times 18.9$$

Multiply 9.81 and 18.9 to get 185.409.

$$\frac{1}{2}x^{2}=\frac{1448402}{15625}+185.409$$

Add \frac{1448402}{15625} and 185.409 to get \frac{34763341}{125000}.

$$\frac{1}{2}x^{2}=\frac{34763341}{125000}$$

Multiply both sides by 2, the reciprocal of \frac{1}{2}.

$$x^{2}=\frac{34763341}{125000}\times 2$$

Multiply \frac{34763341}{125000} and 2 to get \frac{34763341}{62500}.

$$x^{2}=\frac{34763341}{62500}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{34763341}}{250} x=-\frac{\sqrt{34763341}}{250}$$

Steps Using the Quadratic Formula

Calculate 13.616 to the power of 2 and get 185.395456.

$$\frac{1}{2}x^{2}=\frac{1}{2}\times 185.395456+9.81\times 18.9$$

Multiply \frac{1}{2} and 185.395456 to get \frac{1448402}{15625}.

$$\frac{1}{2}x^{2}=\frac{1448402}{15625}+9.81\times 18.9$$

Multiply 9.81 and 18.9 to get 185.409.

$$\frac{1}{2}x^{2}=\frac{1448402}{15625}+185.409$$

Add \frac{1448402}{15625} and 185.409 to get \frac{34763341}{125000}.

$$\frac{1}{2}x^{2}=\frac{34763341}{125000}$$

Subtract \frac{34763341}{125000} from both sides.

$$\frac{1}{2}x^{2}-\frac{34763341}{125000}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{1}{2} for a, 0 for b, and -\frac{34763341}{125000} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{1}{2}\left(-\frac{34763341}{125000}\right)}}{2\times \frac{1}{2}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{1}{2}\left(-\frac{34763341}{125000}\right)}}{2\times \frac{1}{2}}$$

Multiply -4 times \frac{1}{2}.

$$x=\frac{0±\sqrt{-2\left(-\frac{34763341}{125000}\right)}}{2\times \frac{1}{2}}$$

Multiply -2 times -\frac{34763341}{125000}.

$$x=\frac{0±\sqrt{\frac{34763341}{62500}}}{2\times \frac{1}{2}}$$

Take the square root of \frac{34763341}{62500}.

$$x=\frac{0±\frac{\sqrt{34763341}}{250}}{2\times \frac{1}{2}}$$

Multiply 2 times \frac{1}{2}.

$$x=\frac{0±\frac{\sqrt{34763341}}{250}}{1}$$

Now solve the equation x=\frac{0±\frac{\sqrt{34763341}}{250}}{1} when ± is plus.

$$x=\frac{\sqrt{34763341}}{250}$$

Now solve the equation x=\frac{0±\frac{\sqrt{34763341}}{250}}{1} when ± is minus.

$$x=-\frac{\sqrt{34763341}}{250}$$

The equation is now solved.

$$x=\frac{\sqrt{34763341}}{250} x=-\frac{\sqrt{34763341}}{250}$$