Solve 65^2=(16x)^2+(9x)^2

$$65 ^ { 2 } = ( 16 x ) ^ { 2 } + ( 9 x ) ^ { 2 }$$

Solve for x

$$x = \frac{65 \sqrt{337}}{337} \approx 3.54077562$$

$$x = -\frac{65 \sqrt{337}}{337} \approx -3.54077562$$

Steps by Finding Square Root

Calculate 65 to the power of 2 and get 4225.

$$4225=\left(16x\right)^{2}+\left(9x\right)^{2}$$

Expand \left(16x\right)^{2}.

$$4225=16^{2}x^{2}+\left(9x\right)^{2}$$

Calculate 16 to the power of 2 and get 256.

$$4225=256x^{2}+\left(9x\right)^{2}$$

Expand \left(9x\right)^{2}.

$$4225=256x^{2}+9^{2}x^{2}$$

Calculate 9 to the power of 2 and get 81.

$$4225=256x^{2}+81x^{2}$$

Combine 256x^{2} and 81x^{2} to get 337x^{2}.

$$4225=337x^{2}$$

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

$$337x^{2}=4225$$

Divide both sides by 337.

$$x^{2}=\frac{4225}{337}$$

Take the square root of both sides of the equation.

$$x=\frac{65\sqrt{337}}{337} x=-\frac{65\sqrt{337}}{337}$$

Steps Using the Quadratic Formula

Calculate 65 to the power of 2 and get 4225.

$$4225=\left(16x\right)^{2}+\left(9x\right)^{2}$$

Expand \left(16x\right)^{2}.

$$4225=16^{2}x^{2}+\left(9x\right)^{2}$$

Calculate 16 to the power of 2 and get 256.

$$4225=256x^{2}+\left(9x\right)^{2}$$

Expand \left(9x\right)^{2}.

$$4225=256x^{2}+9^{2}x^{2}$$

Calculate 9 to the power of 2 and get 81.

$$4225=256x^{2}+81x^{2}$$

Combine 256x^{2} and 81x^{2} to get 337x^{2}.

$$4225=337x^{2}$$

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

$$337x^{2}=4225$$

Subtract 4225 from both sides.

$$337x^{2}-4225=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 337 for a, 0 for b, and -4225 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 337\left(-4225\right)}}{2\times 337}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 337\left(-4225\right)}}{2\times 337}$$

Multiply -4 times 337.

$$x=\frac{0±\sqrt{-1348\left(-4225\right)}}{2\times 337}$$

Multiply -1348 times -4225.

$$x=\frac{0±\sqrt{5695300}}{2\times 337}$$

Take the square root of 5695300.

$$x=\frac{0±130\sqrt{337}}{2\times 337}$$

Multiply 2 times 337.

$$x=\frac{0±130\sqrt{337}}{674}$$

Now solve the equation x=\frac{0±130\sqrt{337}}{674} when ± is plus.

$$x=\frac{65\sqrt{337}}{337}$$

Now solve the equation x=\frac{0±130\sqrt{337}}{674} when ± is minus.

$$x=-\frac{65\sqrt{337}}{337}$$

The equation is now solved.

$$x=\frac{65\sqrt{337}}{337} x=-\frac{65\sqrt{337}}{337}$$