Solve (7x-3)^2=10

$$( 7 x - 3 ) ^ { 2 } = 10$$

Solve for x

$$x=\frac{\sqrt{10}+3}{7}\approx 0.88032538$$

$$x=\frac{3-\sqrt{10}}{7}\approx -0.023182523$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$7x-3=\sqrt{10} 7x-3=-\sqrt{10}$$

Add 3 to both sides of the equation.

$$7x-3-\left(-3\right)=\sqrt{10}-\left(-3\right) 7x-3-\left(-3\right)=-\sqrt{10}-\left(-3\right)$$

Subtracting -3 from itself leaves 0.

$$7x=\sqrt{10}-\left(-3\right) 7x=-\sqrt{10}-\left(-3\right)$$

Subtract -3 from \sqrt{10}.

$$7x=\sqrt{10}+3$$

Subtract -3 from -\sqrt{10}.

$$7x=3-\sqrt{10}$$

Divide both sides by 7.

$$\frac{7x}{7}=\frac{\sqrt{10}+3}{7} \frac{7x}{7}=\frac{3-\sqrt{10}}{7}$$

Dividing by 7 undoes the multiplication by 7.

$$x=\frac{\sqrt{10}+3}{7} x=\frac{3-\sqrt{10}}{7}$$