Solve (0.8x-240)^2:240=152

$$( 0.8 x - 240 ) ^ { 2 } : 240 = 152$$

Solve for x (complex solution)

$$x=300-10\sqrt{570}\approx 61.253272274$$

$$x=10\left(\sqrt{570}+30\right)\approx 538.746727726$$

Steps by Finding Square Root

Dividing by \frac{1}{240} undoes the multiplication by \frac{1}{240}.

$$\left(0.8x-240\right)^{2}=\frac{152}{\frac{1}{240}}$$

Divide 152 by \frac{1}{240} by multiplying 152 by the reciprocal of \frac{1}{240}.

$$\left(0.8x-240\right)^{2}=36480$$

Take the square root of both sides of the equation.

$$0.8x-240=8\sqrt{570} 0.8x-240=-8\sqrt{570}$$

Add 240 to both sides of the equation.

$$0.8x-240-\left(-240\right)=8\sqrt{570}-\left(-240\right) 0.8x-240-\left(-240\right)=-8\sqrt{570}-\left(-240\right)$$

Subtracting -240 from itself leaves 0.

$$0.8x=8\sqrt{570}-\left(-240\right) 0.8x=-8\sqrt{570}-\left(-240\right)$$

Subtract -240 from 8\sqrt{570}.

$$0.8x=8\sqrt{570}+240$$

Subtract -240 from -8\sqrt{570}.

$$0.8x=240-8\sqrt{570}$$

Divide both sides of the equation by 0.8, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{0.8x}{0.8}=\frac{8\sqrt{570}+240}{0.8} \frac{0.8x}{0.8}=\frac{240-8\sqrt{570}}{0.8}$$

Dividing by 0.8 undoes the multiplication by 0.8.

$$x=\frac{8\sqrt{570}+240}{0.8} x=\frac{240-8\sqrt{570}}{0.8}$$

Divide 8\sqrt{570}+240 by 0.8 by multiplying 8\sqrt{570}+240 by the reciprocal of 0.8.

$$x=10\sqrt{570}+300$$

Divide -8\sqrt{570}+240 by 0.8 by multiplying -8\sqrt{570}+240 by the reciprocal of 0.8.

$$x=300-10\sqrt{570}$$

The equation is now solved.

$$x=10\sqrt{570}+300 x=300-10\sqrt{570}$$

Solve for x

$$x=10\sqrt{570}+300\approx 538.746727726$$

$$x=300-10\sqrt{570}\approx 61.253272274$$

Steps by Finding Square Root

Multiply both sides by 240.

$$\frac{\frac{1}{240}\left(0.8x-240\right)^{2}}{\frac{1}{240}}=\frac{152}{\frac{1}{240}}$$

Dividing by \frac{1}{240} undoes the multiplication by \frac{1}{240}.

$$\left(0.8x-240\right)^{2}=\frac{152}{\frac{1}{240}}$$

Divide 152 by \frac{1}{240} by multiplying 152 by the reciprocal of \frac{1}{240}.

$$\left(0.8x-240\right)^{2}=36480$$

Take the square root of both sides of the equation.

$$0.8x-240=8\sqrt{570} 0.8x-240=-8\sqrt{570}$$

Add 240 to both sides of the equation.

$$0.8x-240-\left(-240\right)=8\sqrt{570}-\left(-240\right) 0.8x-240-\left(-240\right)=-8\sqrt{570}-\left(-240\right)$$

Subtracting -240 from itself leaves 0.

$$0.8x=8\sqrt{570}-\left(-240\right) 0.8x=-8\sqrt{570}-\left(-240\right)$$

Subtract -240 from 8\sqrt{570}.

$$0.8x=8\sqrt{570}+240$$

Subtract -240 from -8\sqrt{570}.

$$0.8x=240-8\sqrt{570}$$

Divide both sides of the equation by 0.8, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{0.8x}{0.8}=\frac{8\sqrt{570}+240}{0.8} \frac{0.8x}{0.8}=\frac{240-8\sqrt{570}}{0.8}$$

Dividing by 0.8 undoes the multiplication by 0.8.

$$x=\frac{8\sqrt{570}+240}{0.8} x=\frac{240-8\sqrt{570}}{0.8}$$

Divide 8\sqrt{570}+240 by 0.8 by multiplying 8\sqrt{570}+240 by the reciprocal of 0.8.

$$x=10\sqrt{570}+300$$

Divide -8\sqrt{570}+240 by 0.8 by multiplying -8\sqrt{570}+240 by the reciprocal of 0.8.

$$x=300-10\sqrt{570}$$

The equation is now solved.

$$x=10\sqrt{570}+300 x=300-10\sqrt{570}$$