Solve 3^2+(8x)^2=(17x)^2

$$3 ^ { 2 } + ( 8 x ) ^ { 2 } = ( 17 x ) ^ { 2 }$$

Solve for x

$$x=\frac{1}{5}=0.2$$

$$x=-\frac{1}{5}=-0.2$$

Steps by Finding Square Root

Calculate 3 to the power of 2 and get 9.

$$9+\left(8x\right)^{2}=\left(17x\right)^{2}$$

Expand \left(8x\right)^{2}.

$$9+8^{2}x^{2}=\left(17x\right)^{2}$$

Calculate 8 to the power of 2 and get 64.

$$9+64x^{2}=\left(17x\right)^{2}$$

Expand \left(17x\right)^{2}.

$$9+64x^{2}=17^{2}x^{2}$$

Calculate 17 to the power of 2 and get 289.

$$9+64x^{2}=289x^{2}$$

Subtract 289x^{2} from both sides.

$$9+64x^{2}-289x^{2}=0$$

Combine 64x^{2} and -289x^{2} to get -225x^{2}.

$$9-225x^{2}=0$$

Subtract 9 from both sides. Anything subtracted from zero gives its negation.

$$-225x^{2}=-9$$

Divide both sides by -225.

$$x^{2}=\frac{-9}{-225}$$

Reduce the fraction \frac{-9}{-225} to lowest terms by extracting and canceling out -9.

$$x^{2}=\frac{1}{25}$$

Take the square root of both sides of the equation.

$$x=\frac{1}{5} x=-\frac{1}{5}$$

Steps Using the Quadratic Formula

Calculate 3 to the power of 2 and get 9.

$$9+\left(8x\right)^{2}=\left(17x\right)^{2}$$

Expand \left(8x\right)^{2}.

$$9+8^{2}x^{2}=\left(17x\right)^{2}$$

Calculate 8 to the power of 2 and get 64.

$$9+64x^{2}=\left(17x\right)^{2}$$

Expand \left(17x\right)^{2}.

$$9+64x^{2}=17^{2}x^{2}$$

Calculate 17 to the power of 2 and get 289.

$$9+64x^{2}=289x^{2}$$

Subtract 289x^{2} from both sides.

$$9+64x^{2}-289x^{2}=0$$

Combine 64x^{2} and -289x^{2} to get -225x^{2}.

$$9-225x^{2}=0$$

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.

$$-225x^{2}+9=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -225 for a, 0 for b, and 9 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-225\right)\times 9}}{2\left(-225\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-225\right)\times 9}}{2\left(-225\right)}$$

Multiply -4 times -225.

$$x=\frac{0±\sqrt{900\times 9}}{2\left(-225\right)}$$

Multiply 900 times 9.

$$x=\frac{0±\sqrt{8100}}{2\left(-225\right)}$$

Take the square root of 8100.

$$x=\frac{0±90}{2\left(-225\right)}$$

Multiply 2 times -225.

$$x=\frac{0±90}{-450}$$

Now solve the equation x=\frac{0±90}{-450} when ± is plus. Reduce the fraction \frac{90}{-450} to lowest terms by extracting and canceling out 90.

$$x=-\frac{1}{5}$$

Now solve the equation x=\frac{0±90}{-450} when ± is minus. Reduce the fraction \frac{-90}{-450} to lowest terms by extracting and canceling out 90.

$$x=\frac{1}{5}$$

The equation is now solved.

$$x=-\frac{1}{5} x=\frac{1}{5}$$