Solve 4(8-5x)^2-49=-24

$$4 ( 8 - 5 x ) ^ { 2 } - 49 = - 24$$

Solve for x

$$x = \frac{11}{10} = 1\frac{1}{10} = 1.1$$

$$x = \frac{21}{10} = 2\frac{1}{10} = 2.1$$

Steps by Finding Square Root

Add 49 to both sides of the equation.

$$4\left(-5x+8\right)^{2}-49+49=-24+49$$

Subtracting 49 from itself leaves 0.

$$4\left(-5x+8\right)^{2}=-24+49$$

Add -24 to 49.

$$4\left(-5x+8\right)^{2}=25$$

Divide both sides by 4.

$$\frac{4\left(-5x+8\right)^{2}}{4}=\frac{25}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$\left(-5x+8\right)^{2}=\frac{25}{4}$$

Take the square root of both sides of the equation.

$$-5x+8=\frac{5}{2} -5x+8=-\frac{5}{2}$$

Subtract 8 from both sides of the equation.

$$-5x+8-8=\frac{5}{2}-8 -5x+8-8=-\frac{5}{2}-8$$

Subtracting 8 from itself leaves 0.

$$-5x=\frac{5}{2}-8 -5x=-\frac{5}{2}-8$$

Subtract 8 from \frac{5}{2}.

$$-5x=-\frac{11}{2}$$

Subtract 8 from -\frac{5}{2}.

$$-5x=-\frac{21}{2}$$

Divide both sides by -5.

$$\frac{-5x}{-5}=-\frac{\frac{11}{2}}{-5} \frac{-5x}{-5}=-\frac{\frac{21}{2}}{-5}$$

Dividing by -5 undoes the multiplication by -5.

$$x=-\frac{\frac{11}{2}}{-5} x=-\frac{\frac{21}{2}}{-5}$$

Divide -\frac{11}{2} by -5.

$$x=\frac{11}{10}$$

Divide -\frac{21}{2} by -5.

$$x=\frac{21}{10}$$

The equation is now solved.

$$x=\frac{11}{10} x=\frac{21}{10}$$