Solve 100=8^2+x^2

$$100 = 8 ^ { 2 } + x ^ { 2 }$$

Solve for x

$$x=6$$

$$x=-6$$

Steps Using Difference of Squares

Calculate 8 to the power of 2 and get 64.

$$100=64+x^{2}$$

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

$$64+x^{2}=100$$

Subtract 100 from both sides.

$$64+x^{2}-100=0$$

Subtract 100 from 64 to get -36.

$$-36+x^{2}=0$$

Consider -36+x^{2}. Rewrite -36+x^{2} as x^{2}-6^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-6\right)\left(x+6\right)=0$$

To find equation solutions, solve x-6=0 and x+6=0.

$$x=6 x=-6$$

Steps by Finding Square Root

Calculate 8 to the power of 2 and get 64.

$$100=64+x^{2}$$

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

$$64+x^{2}=100$$

Subtract 64 from both sides.

$$x^{2}=100-64$$

Subtract 64 from 100 to get 36.

$$x^{2}=36$$

Take the square root of both sides of the equation.

$$x=6 x=-6$$

Steps Using the Quadratic Formula

Calculate 8 to the power of 2 and get 64.

$$100=64+x^{2}$$

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

$$64+x^{2}=100$$

Subtract 100 from both sides.

$$64+x^{2}-100=0$$

Subtract 100 from 64 to get -36.

$$-36+x^{2}=0$$

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.

$$x^{2}-36=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -36 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-36\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-36\right)}}{2}$$

Multiply -4 times -36.

$$x=\frac{0±\sqrt{144}}{2}$$

Take the square root of 144.

$$x=\frac{0±12}{2}$$

Now solve the equation x=\frac{0±12}{2} when ± is plus. Divide 12 by 2.

$$x=6$$

Now solve the equation x=\frac{0±12}{2} when ± is minus. Divide -12 by 2.

$$x=-6$$

The equation is now solved.

$$x=6 x=-6$$