Solve 32^2+x^2=88^2

$$32 ^ { 2 } + x ^ { 2 } = 88 ^ { 2 }$$

Solve for x

$$x=8\sqrt{105}\approx 81.975606128$$

$$x=-8\sqrt{105}\approx -81.975606128$$

Steps by Finding Square Root

Calculate 32 to the power of 2 and get 1024.

$$1024+x^{2}=88^{2}$$

Calculate 88 to the power of 2 and get 7744.

$$1024+x^{2}=7744$$

Subtract 1024 from both sides.

$$x^{2}=7744-1024$$

Subtract 1024 from 7744 to get 6720.

$$x^{2}=6720$$

Take the square root of both sides of the equation.

$$x=8\sqrt{105} x=-8\sqrt{105}$$

Steps Using the Quadratic Formula

Calculate 32 to the power of 2 and get 1024.

$$1024+x^{2}=88^{2}$$

Calculate 88 to the power of 2 and get 7744.

$$1024+x^{2}=7744$$

Subtract 7744 from both sides.

$$1024+x^{2}-7744=0$$

Subtract 7744 from 1024 to get -6720.

$$-6720+x^{2}=0$$

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.

$$x^{2}-6720=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -6720 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-6720\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-6720\right)}}{2}$$

Multiply -4 times -6720.

$$x=\frac{0±\sqrt{26880}}{2}$$

Take the square root of 26880.

$$x=\frac{0±16\sqrt{105}}{2}$$

Now solve the equation x=\frac{0±16\sqrt{105}}{2} when ± is plus.

$$x=8\sqrt{105}$$

Now solve the equation x=\frac{0±16\sqrt{105}}{2} when ± is minus.

$$x=-8\sqrt{105}$$

The equation is now solved.

$$x=8\sqrt{105} x=-8\sqrt{105}$$