Solve (16^2+9^2)*x^2=133^2

$$( { 16 }^{ 2 } + { 9 }^{ 2 } ) \times { x }^{ 2 } = { 133 }^{ 2 }$$

Solve for x

$$x = \frac{133 \sqrt{337}}{337} \approx 7.244971652$$

$$x = -\frac{133 \sqrt{337}}{337} \approx -7.244971652$$

Steps by Finding Square Root

Calculate 16 to the power of 2 and get 256.

$$\left(256+9^{2}\right)x^{2}=133^{2}$$

Calculate 9 to the power of 2 and get 81.

$$\left(256+81\right)x^{2}=133^{2}$$

Add 256 and 81 to get 337.

$$337x^{2}=133^{2}$$

Calculate 133 to the power of 2 and get 17689.

$$337x^{2}=17689$$

Divide both sides by 337.

$$x^{2}=\frac{17689}{337}$$

Take the square root of both sides of the equation.

$$x=\frac{133\sqrt{337}}{337} x=-\frac{133\sqrt{337}}{337}$$

Steps Using the Quadratic Formula

Calculate 16 to the power of 2 and get 256.

$$\left(256+9^{2}\right)x^{2}=133^{2}$$

Calculate 9 to the power of 2 and get 81.

$$\left(256+81\right)x^{2}=133^{2}$$

Add 256 and 81 to get 337.

$$337x^{2}=133^{2}$$

Calculate 133 to the power of 2 and get 17689.

$$337x^{2}=17689$$

Subtract 17689 from both sides.

$$337x^{2}-17689=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 337 for a, 0 for b, and -17689 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 337\left(-17689\right)}}{2\times 337}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 337\left(-17689\right)}}{2\times 337}$$

Multiply -4 times 337.

$$x=\frac{0±\sqrt{-1348\left(-17689\right)}}{2\times 337}$$

Multiply -1348 times -17689.

$$x=\frac{0±\sqrt{23844772}}{2\times 337}$$

Take the square root of 23844772.

$$x=\frac{0±266\sqrt{337}}{2\times 337}$$

Multiply 2 times 337.

$$x=\frac{0±266\sqrt{337}}{674}$$

Now solve the equation x=\frac{0±266\sqrt{337}}{674} when ± is plus.

$$x=\frac{133\sqrt{337}}{337}$$

Now solve the equation x=\frac{0±266\sqrt{337}}{674} when ± is minus.

$$x=-\frac{133\sqrt{337}}{337}$$

The equation is now solved.

$$x=\frac{133\sqrt{337}}{337} x=-\frac{133\sqrt{337}}{337}$$