Solve (96)^2+(63)^2=x^2-(111)^2-8350

$$( 96 ) ^ { 2 } + ( 63 ) ^ { 2 } = x ^ { 2 } - ( 111 ) ^ { 2 } - 8350$$

Solve for x

$$x=184$$

$$x=-184$$

Steps Using Difference of Squares

Calculate 96 to the power of 2 and get 9216.

$$9216+63^{2}=x^{2}-111^{2}-8350$$

Calculate 63 to the power of 2 and get 3969.

$$9216+3969=x^{2}-111^{2}-8350$$

Add 9216 and 3969 to get 13185.

$$13185=x^{2}-111^{2}-8350$$

Calculate 111 to the power of 2 and get 12321.

$$13185=x^{2}-12321-8350$$

Subtract 8350 from -12321 to get -20671.

$$13185=x^{2}-20671$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}-20671=13185$$

Subtract 13185 from both sides.

$$x^{2}-20671-13185=0$$

Subtract 13185 from -20671 to get -33856.

$$x^{2}-33856=0$$

Consider x^{2}-33856. Rewrite x^{2}-33856 as x^{2}-184^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-184\right)\left(x+184\right)=0$$

To find equation solutions, solve x-184=0 and x+184=0.

$$x=184 x=-184$$

Steps by Finding Square Root

Calculate 96 to the power of 2 and get 9216.

$$9216+63^{2}=x^{2}-111^{2}-8350$$

Calculate 63 to the power of 2 and get 3969.

$$9216+3969=x^{2}-111^{2}-8350$$

Add 9216 and 3969 to get 13185.

$$13185=x^{2}-111^{2}-8350$$

Calculate 111 to the power of 2 and get 12321.

$$13185=x^{2}-12321-8350$$

Subtract 8350 from -12321 to get -20671.

$$13185=x^{2}-20671$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}-20671=13185$$

Add 20671 to both sides.

$$x^{2}=13185+20671$$

Add 13185 and 20671 to get 33856.

$$x^{2}=33856$$

Take the square root of both sides of the equation.

$$x=184 x=-184$$

Steps Using the Quadratic Formula

Calculate 96 to the power of 2 and get 9216.

$$9216+63^{2}=x^{2}-111^{2}-8350$$

Calculate 63 to the power of 2 and get 3969.

$$9216+3969=x^{2}-111^{2}-8350$$

Add 9216 and 3969 to get 13185.

$$13185=x^{2}-111^{2}-8350$$

Calculate 111 to the power of 2 and get 12321.

$$13185=x^{2}-12321-8350$$

Subtract 8350 from -12321 to get -20671.

$$13185=x^{2}-20671$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}-20671=13185$$

Subtract 13185 from both sides.

$$x^{2}-20671-13185=0$$

Subtract 13185 from -20671 to get -33856.

$$x^{2}-33856=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -33856 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-33856\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-33856\right)}}{2}$$

Multiply -4 times -33856.

$$x=\frac{0±\sqrt{135424}}{2}$$

Take the square root of 135424.

$$x=\frac{0±368}{2}$$

Now solve the equation x=\frac{0±368}{2} when ± is plus. Divide 368 by 2.

$$x=184$$

Now solve the equation x=\frac{0±368}{2} when ± is minus. Divide -368 by 2.

$$x=-184$$

The equation is now solved.

$$x=184 x=-184$$