Solve 17^2=8^2+x^2

$$17 ^ { 2 } = 8 ^ { 2 } + x ^ { 2 }$$

Solve for x

$$x=15$$

$$x=-15$$

Steps Using Difference of Squares

Calculate 17 to the power of 2 and get 289.

$$289=8^{2}+x^{2}$$

Calculate 8 to the power of 2 and get 64.

$$289=64+x^{2}$$

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

$$64+x^{2}=289$$

Subtract 289 from both sides.

$$64+x^{2}-289=0$$

Subtract 289 from 64 to get -225.

$$-225+x^{2}=0$$

Consider -225+x^{2}. Rewrite -225+x^{2} as x^{2}-15^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-15\right)\left(x+15\right)=0$$

To find equation solutions, solve x-15=0 and x+15=0.

$$x=15 x=-15$$

Steps by Finding Square Root

Calculate 17 to the power of 2 and get 289.

$$289=8^{2}+x^{2}$$

Calculate 8 to the power of 2 and get 64.

$$289=64+x^{2}$$

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

$$64+x^{2}=289$$

Subtract 64 from both sides.

$$x^{2}=289-64$$

Subtract 64 from 289 to get 225.

$$x^{2}=225$$

Take the square root of both sides of the equation.

$$x=15 x=-15$$

Steps Using the Quadratic Formula

Calculate 17 to the power of 2 and get 289.

$$289=8^{2}+x^{2}$$

Calculate 8 to the power of 2 and get 64.

$$289=64+x^{2}$$

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

$$64+x^{2}=289$$

Subtract 289 from both sides.

$$64+x^{2}-289=0$$

Subtract 289 from 64 to get -225.

$$-225+x^{2}=0$$

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.

$$x^{2}-225=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -225 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-225\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-225\right)}}{2}$$

Multiply -4 times -225.

$$x=\frac{0±\sqrt{900}}{2}$$

Take the square root of 900.

$$x=\frac{0±30}{2}$$

Now solve the equation x=\frac{0±30}{2} when ± is plus. Divide 30 by 2.

$$x=15$$

Now solve the equation x=\frac{0±30}{2} when ± is minus. Divide -30 by 2.

$$x=-15$$

The equation is now solved.

$$x=15 x=-15$$