Solve 4(8x-1)^2=49

$$4 ( 8 x - 1 ) ^ { 2 } = 49$$

Solve for x

$$x=\frac{9}{16}=0.5625$$

$$x=-\frac{5}{16}=-0.3125$$

Steps by Finding Square Root

Divide both sides by 4.

$$\frac{4\left(8x-1\right)^{2}}{4}=\frac{49}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$\left(8x-1\right)^{2}=\frac{49}{4}$$

Take the square root of both sides of the equation.

$$8x-1=\frac{7}{2} 8x-1=-\frac{7}{2}$$

Add 1 to both sides of the equation.

$$8x-1-\left(-1\right)=\frac{7}{2}-\left(-1\right) 8x-1-\left(-1\right)=-\frac{7}{2}-\left(-1\right)$$

Subtracting -1 from itself leaves 0.

$$8x=\frac{7}{2}-\left(-1\right) 8x=-\frac{7}{2}-\left(-1\right)$$

Subtract -1 from \frac{7}{2}.

$$8x=\frac{9}{2}$$

Subtract -1 from -\frac{7}{2}.

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

Divide both sides by 8.

$$\frac{8x}{8}=\frac{\frac{9}{2}}{8} \frac{8x}{8}=-\frac{\frac{5}{2}}{8}$$

Dividing by 8 undoes the multiplication by 8.

$$x=\frac{\frac{9}{2}}{8} x=-\frac{\frac{5}{2}}{8}$$

Divide \frac{9}{2} by 8.

$$x=\frac{9}{16}$$

Divide -\frac{5}{2} by 8.

$$x=-\frac{5}{16}$$

The equation is now solved.

$$x=\frac{9}{16} x=-\frac{5}{16}$$