Solve {left(16*x/10right)}^2+x^2=43.18^2

$${ \left( \frac{ 16 \times x }{ 10 } \right) }^{ 2 } + { x }^{ 2 } = { 43.18 }^{ 2 }$$

Solve for x

$$x = \frac{2159 \sqrt{89}}{890} \approx 22.885354229$$

$$x = -\frac{2159 \sqrt{89}}{890} \approx -22.885354229$$

Steps by Finding Square Root

Divide 16x by 10 to get \frac{8}{5}x.

$$\left(\frac{8}{5}x\right)^{2}+x^{2}=43.18^{2}$$

Expand \left(\frac{8}{5}x\right)^{2}.

$$\left(\frac{8}{5}\right)^{2}x^{2}+x^{2}=43.18^{2}$$

Calculate \frac{8}{5} to the power of 2 and get \frac{64}{25}.

$$\frac{64}{25}x^{2}+x^{2}=43.18^{2}$$

Combine \frac{64}{25}x^{2} and x^{2} to get \frac{89}{25}x^{2}.

$$\frac{89}{25}x^{2}=43.18^{2}$$

Calculate 43.18 to the power of 2 and get 1864.5124.

$$\frac{89}{25}x^{2}=1864.5124$$

Multiply both sides by \frac{25}{89}, the reciprocal of \frac{89}{25}.

$$x^{2}=1864.5124\times \frac{25}{89}$$

Multiply 1864.5124 and \frac{25}{89} to get \frac{4661281}{8900}.

$$x^{2}=\frac{4661281}{8900}$$

Take the square root of both sides of the equation.

$$x=\frac{2159\sqrt{89}}{890} x=-\frac{2159\sqrt{89}}{890}$$

Steps Using the Quadratic Formula

Divide 16x by 10 to get \frac{8}{5}x.

$$\left(\frac{8}{5}x\right)^{2}+x^{2}=43.18^{2}$$

Expand \left(\frac{8}{5}x\right)^{2}.

$$\left(\frac{8}{5}\right)^{2}x^{2}+x^{2}=43.18^{2}$$

Calculate \frac{8}{5} to the power of 2 and get \frac{64}{25}.

$$\frac{64}{25}x^{2}+x^{2}=43.18^{2}$$

Combine \frac{64}{25}x^{2} and x^{2} to get \frac{89}{25}x^{2}.

$$\frac{89}{25}x^{2}=43.18^{2}$$

Calculate 43.18 to the power of 2 and get 1864.5124.

$$\frac{89}{25}x^{2}=1864.5124$$

Subtract 1864.5124 from both sides.

$$\frac{89}{25}x^{2}-1864.5124=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{89}{25} for a, 0 for b, and -1864.5124 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{89}{25}\left(-1864.5124\right)}}{2\times \frac{89}{25}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{89}{25}\left(-1864.5124\right)}}{2\times \frac{89}{25}}$$

Multiply -4 times \frac{89}{25}.

$$x=\frac{0±\sqrt{-\frac{356}{25}\left(-1864.5124\right)}}{2\times \frac{89}{25}}$$

Multiply -\frac{356}{25} times -1864.5124 by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$x=\frac{0±\sqrt{\frac{414854009}{15625}}}{2\times \frac{89}{25}}$$

Take the square root of \frac{414854009}{15625}.

$$x=\frac{0±\frac{2159\sqrt{89}}{125}}{2\times \frac{89}{25}}$$

Multiply 2 times \frac{89}{25}.

$$x=\frac{0±\frac{2159\sqrt{89}}{125}}{\frac{178}{25}}$$

Now solve the equation x=\frac{0±\frac{2159\sqrt{89}}{125}}{\frac{178}{25}} when ± is plus.

$$x=\frac{2159\sqrt{89}}{890}$$

Now solve the equation x=\frac{0±\frac{2159\sqrt{89}}{125}}{\frac{178}{25}} when ± is minus.

$$x=-\frac{2159\sqrt{89}}{890}$$

The equation is now solved.

$$x=\frac{2159\sqrt{89}}{890} x=-\frac{2159\sqrt{89}}{890}$$