Solve (16^2+9^2)*x^2=13.3^2

$$( { 16 }^{ 2 } + { 9 }^{ 2 } ) \times { x }^{ 2 } = { 13.3 }^{ 2 }$$

Solve for x

$$x=\frac{133\sqrt{337}}{3370}\approx 0.724497165$$

$$x=-\frac{133\sqrt{337}}{3370}\approx -0.724497165$$

Steps by Finding Square Root

Calculate 16 to the power of 2 and get 256.

$$\left(256+9^{2}\right)x^{2}=13.3^{2}$$

Calculate 9 to the power of 2 and get 81.

$$\left(256+81\right)x^{2}=13.3^{2}$$

Add 256 and 81 to get 337.

$$337x^{2}=13.3^{2}$$

Calculate 13.3 to the power of 2 and get 176.89.

$$337x^{2}=176.89$$

Divide both sides by 337.

$$x^{2}=\frac{176.89}{337}$$

Expand \frac{176.89}{337} by multiplying both numerator and the denominator by 100.

$$x^{2}=\frac{17689}{33700}$$

Take the square root of both sides of the equation.

$$x=\frac{133\sqrt{337}}{3370} x=-\frac{133\sqrt{337}}{3370}$$

Steps Using the Quadratic Formula

Calculate 16 to the power of 2 and get 256.

$$\left(256+9^{2}\right)x^{2}=13.3^{2}$$

Calculate 9 to the power of 2 and get 81.

$$\left(256+81\right)x^{2}=13.3^{2}$$

Add 256 and 81 to get 337.

$$337x^{2}=13.3^{2}$$

Calculate 13.3 to the power of 2 and get 176.89.

$$337x^{2}=176.89$$

Subtract 176.89 from both sides.

$$337x^{2}-176.89=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 337 for a, 0 for b, and -176.89 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 337\left(-176.89\right)}}{2\times 337}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 337\left(-176.89\right)}}{2\times 337}$$

Multiply -4 times 337.

$$x=\frac{0±\sqrt{-1348\left(-176.89\right)}}{2\times 337}$$

Multiply -1348 times -176.89.

$$x=\frac{0±\sqrt{238447.72}}{2\times 337}$$

Take the square root of 238447.72.

$$x=\frac{0±\frac{133\sqrt{337}}{5}}{2\times 337}$$

Multiply 2 times 337.

$$x=\frac{0±\frac{133\sqrt{337}}{5}}{674}$$

Now solve the equation x=\frac{0±\frac{133\sqrt{337}}{5}}{674} when ± is plus.

$$x=\frac{133\sqrt{337}}{3370}$$

Now solve the equation x=\frac{0±\frac{133\sqrt{337}}{5}}{674} when ± is minus.

$$x=-\frac{133\sqrt{337}}{3370}$$

The equation is now solved.

$$x=\frac{133\sqrt{337}}{3370} x=-\frac{133\sqrt{337}}{3370}$$