Solve 0.8^2+(16/5x)^2=1.6^2

$$0.8 ^ { 2 } + ( \frac { 16 } { 5 } x ) ^ { 2 } = 1.6 ^ { 2 }$$

Solve for x

$$x=\frac{\sqrt{3}}{4}\approx 0.433012702$$

$$x=-\frac{\sqrt{3}}{4}\approx -0.433012702$$

Steps by Finding Square Root

Calculate 0.8 to the power of 2 and get 0.64.

$$0.64+\left(\frac{16}{5}x\right)^{2}=1.6^{2}$$

Expand \left(\frac{16}{5}x\right)^{2}.

$$0.64+\left(\frac{16}{5}\right)^{2}x^{2}=1.6^{2}$$

Calculate \frac{16}{5} to the power of 2 and get \frac{256}{25}.

$$0.64+\frac{256}{25}x^{2}=1.6^{2}$$

Calculate 1.6 to the power of 2 and get 2.56.

$$0.64+\frac{256}{25}x^{2}=2.56$$

Subtract 0.64 from both sides.

$$\frac{256}{25}x^{2}=2.56-0.64$$

Subtract 0.64 from 2.56 to get 1.92.

$$\frac{256}{25}x^{2}=1.92$$

Multiply both sides by \frac{25}{256}, the reciprocal of \frac{256}{25}.

$$x^{2}=1.92\times \frac{25}{256}$$

Multiply 1.92 and \frac{25}{256} to get \frac{3}{16}.

$$x^{2}=\frac{3}{16}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{3}}{4} x=-\frac{\sqrt{3}}{4}$$

Steps Using the Quadratic Formula

Calculate 0.8 to the power of 2 and get 0.64.

$$0.64+\left(\frac{16}{5}x\right)^{2}=1.6^{2}$$

Expand \left(\frac{16}{5}x\right)^{2}.

$$0.64+\left(\frac{16}{5}\right)^{2}x^{2}=1.6^{2}$$

Calculate \frac{16}{5} to the power of 2 and get \frac{256}{25}.

$$0.64+\frac{256}{25}x^{2}=1.6^{2}$$

Calculate 1.6 to the power of 2 and get 2.56.

$$0.64+\frac{256}{25}x^{2}=2.56$$

Subtract 2.56 from both sides.

$$0.64+\frac{256}{25}x^{2}-2.56=0$$

Subtract 2.56 from 0.64 to get -1.92.

$$-1.92+\frac{256}{25}x^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$\frac{256}{25}x^{2}-1.92=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{256}{25} for a, 0 for b, and -1.92 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{256}{25}\left(-1.92\right)}}{2\times \frac{256}{25}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{256}{25}\left(-1.92\right)}}{2\times \frac{256}{25}}$$

Multiply -4 times \frac{256}{25}.

$$x=\frac{0±\sqrt{-\frac{1024}{25}\left(-1.92\right)}}{2\times \frac{256}{25}}$$

Multiply -\frac{1024}{25} times -1.92 by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$x=\frac{0±\sqrt{\frac{49152}{625}}}{2\times \frac{256}{25}}$$

Take the square root of \frac{49152}{625}.

$$x=\frac{0±\frac{128\sqrt{3}}{25}}{2\times \frac{256}{25}}$$

Multiply 2 times \frac{256}{25}.

$$x=\frac{0±\frac{128\sqrt{3}}{25}}{\frac{512}{25}}$$

Now solve the equation x=\frac{0±\frac{128\sqrt{3}}{25}}{\frac{512}{25}} when ± is plus.

$$x=\frac{\sqrt{3}}{4}$$

Now solve the equation x=\frac{0±\frac{128\sqrt{3}}{25}}{\frac{512}{25}} when ± is minus.

$$x=-\frac{\sqrt{3}}{4}$$

The equation is now solved.

$$x=\frac{\sqrt{3}}{4} x=-\frac{\sqrt{3}}{4}$$