Solve 99^2+x^2=125^2

$${ 99 }^{ 2 } + { x }^{ 2 } = { 125 }^{ 2 }$$

Solve for x

$$x=8\sqrt{91}\approx 76.315136113$$

$$x=-8\sqrt{91}\approx -76.315136113$$

Steps by Finding Square Root

Calculate 99 to the power of 2 and get 9801.

$$9801+x^{2}=125^{2}$$

Calculate 125 to the power of 2 and get 15625.

$$9801+x^{2}=15625$$

Subtract 9801 from both sides.

$$x^{2}=15625-9801$$

Subtract 9801 from 15625 to get 5824.

$$x^{2}=5824$$

Take the square root of both sides of the equation.

$$x=8\sqrt{91} x=-8\sqrt{91}$$

Steps Using the Quadratic Formula

Calculate 99 to the power of 2 and get 9801.

$$9801+x^{2}=125^{2}$$

Calculate 125 to the power of 2 and get 15625.

$$9801+x^{2}=15625$$

Subtract 15625 from both sides.

$$9801+x^{2}-15625=0$$

Subtract 15625 from 9801 to get -5824.

$$-5824+x^{2}=0$$

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.

$$x^{2}-5824=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -5824 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-5824\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-5824\right)}}{2}$$

Multiply -4 times -5824.

$$x=\frac{0±\sqrt{23296}}{2}$$

Take the square root of 23296.

$$x=\frac{0±16\sqrt{91}}{2}$$

Now solve the equation x=\frac{0±16\sqrt{91}}{2} when ± is plus.

$$x=8\sqrt{91}$$

Now solve the equation x=\frac{0±16\sqrt{91}}{2} when ± is minus.

$$x=-8\sqrt{91}$$

The equation is now solved.

$$x=8\sqrt{91} x=-8\sqrt{91}$$