Solve 9.9^2+x^2=12.5^2

$${ 9.9 }^{ 2 } + { x }^{ 2 } = { 12.5 }^{ 2 }$$

Solve for x

$$x = \frac{4 \sqrt{91}}{5} \approx 7.631513611$$

$$x = -\frac{4 \sqrt{91}}{5} \approx -7.631513611$$

Steps by Finding Square Root

Calculate 9.9 to the power of 2 and get 98.01.

$$98.01+x^{2}=12.5^{2}$$

Calculate 12.5 to the power of 2 and get 156.25.

$$98.01+x^{2}=156.25$$

Subtract 98.01 from both sides.

$$x^{2}=156.25-98.01$$

Subtract 98.01 from 156.25 to get 58.24.

$$x^{2}=58.24$$

Take the square root of both sides of the equation.

$$x=\frac{4\sqrt{91}}{5} x=-\frac{4\sqrt{91}}{5}$$

Steps Using the Quadratic Formula

Calculate 9.9 to the power of 2 and get 98.01.

$$98.01+x^{2}=12.5^{2}$$

Calculate 12.5 to the power of 2 and get 156.25.

$$98.01+x^{2}=156.25$$

Subtract 156.25 from both sides.

$$98.01+x^{2}-156.25=0$$

Subtract 156.25 from 98.01 to get -58.24.

$$-58.24+x^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$x^{2}-58.24=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -58.24 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-58.24\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-58.24\right)}}{2}$$

Multiply -4 times -58.24.

$$x=\frac{0±\sqrt{232.96}}{2}$$

Take the square root of 232.96.

$$x=\frac{0±\frac{8\sqrt{91}}{5}}{2}$$

Now solve the equation x=\frac{0±\frac{8\sqrt{91}}{5}}{2} when ± is plus.

$$x=\frac{4\sqrt{91}}{5}$$

Now solve the equation x=\frac{0±\frac{8\sqrt{91}}{5}}{2} when ± is minus.

$$x=-\frac{4\sqrt{91}}{5}$$

The equation is now solved.

$$x=\frac{4\sqrt{91}}{5} x=-\frac{4\sqrt{91}}{5}$$