Solve 16=x^2+{left(3x/10right)}^2

$$16 = { x }^{ 2 } + { \left( \frac{ 3x }{ 10 } \right) }^{ 2 }$$

Solve for x

$$x = \frac{40 \sqrt{109}}{109} \approx 3.831305141$$

$$x = -\frac{40 \sqrt{109}}{109} \approx -3.831305141$$

Steps by Finding Square Root

To raise \frac{3x}{10} to a power, raise both numerator and denominator to the power and then divide.

$$16=x^{2}+\frac{\left(3x\right)^{2}}{10^{2}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{2} times \frac{10^{2}}{10^{2}}.

$$16=\frac{x^{2}\times 10^{2}}{10^{2}}+\frac{\left(3x\right)^{2}}{10^{2}}$$

Since \frac{x^{2}\times 10^{2}}{10^{2}} and \frac{\left(3x\right)^{2}}{10^{2}} have the same denominator, add them by adding their numerators.

$$16=\frac{x^{2}\times 10^{2}+\left(3x\right)^{2}}{10^{2}}$$

Do the multiplications in x^{2}\times 10^{2}+\left(3x\right)^{2}.

$$16=\frac{100x^{2}+\left(3x\right)^{2}}{10^{2}}$$

Combine like terms in 100x^{2}+\left(3x\right)^{2}.

$$16=\frac{109x^{2}}{10^{2}}$$

Calculate 10 to the power of 2 and get 100.

$$16=\frac{109x^{2}}{100}$$

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

$$\frac{109x^{2}}{100}=16$$

Multiply both sides by 100.

$$109x^{2}=16\times 100$$

Multiply 16 and 100 to get 1600.

$$109x^{2}=1600$$

Divide both sides by 109.

$$x^{2}=\frac{1600}{109}$$

Take the square root of both sides of the equation.

$$x=\frac{40\sqrt{109}}{109} x=-\frac{40\sqrt{109}}{109}$$

Steps Using the Quadratic Formula

To raise \frac{3x}{10} to a power, raise both numerator and denominator to the power and then divide.

$$16=x^{2}+\frac{\left(3x\right)^{2}}{10^{2}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{2} times \frac{10^{2}}{10^{2}}.

$$16=\frac{x^{2}\times 10^{2}}{10^{2}}+\frac{\left(3x\right)^{2}}{10^{2}}$$

Since \frac{x^{2}\times 10^{2}}{10^{2}} and \frac{\left(3x\right)^{2}}{10^{2}} have the same denominator, add them by adding their numerators.

$$16=\frac{x^{2}\times 10^{2}+\left(3x\right)^{2}}{10^{2}}$$

Do the multiplications in x^{2}\times 10^{2}+\left(3x\right)^{2}.

$$16=\frac{100x^{2}+\left(3x\right)^{2}}{10^{2}}$$

Combine like terms in 100x^{2}+\left(3x\right)^{2}.

$$16=\frac{109x^{2}}{10^{2}}$$

Calculate 10 to the power of 2 and get 100.

$$16=\frac{109x^{2}}{100}$$

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

$$\frac{109x^{2}}{100}=16$$

Subtract 16 from both sides.

$$\frac{109x^{2}}{100}-16=0$$

Multiply both sides of the equation by 100.

$$109x^{2}-1600=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 109 for a, 0 for b, and -1600 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 109\left(-1600\right)}}{2\times 109}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 109\left(-1600\right)}}{2\times 109}$$

Multiply -4 times 109.

$$x=\frac{0±\sqrt{-436\left(-1600\right)}}{2\times 109}$$

Multiply -436 times -1600.

$$x=\frac{0±\sqrt{697600}}{2\times 109}$$

Take the square root of 697600.

$$x=\frac{0±80\sqrt{109}}{2\times 109}$$

Multiply 2 times 109.

$$x=\frac{0±80\sqrt{109}}{218}$$

Now solve the equation x=\frac{0±80\sqrt{109}}{218} when ± is plus.

$$x=\frac{40\sqrt{109}}{109}$$

Now solve the equation x=\frac{0±80\sqrt{109}}{218} when ± is minus.

$$x=-\frac{40\sqrt{109}}{109}$$

The equation is now solved.

$$x=\frac{40\sqrt{109}}{109} x=-\frac{40\sqrt{109}}{109}$$