Solve 3(x-1)^2-5=16

$$3 ( x - 1 ) ^ { 2 } - 5 = 16$$

Solve for x

$$x=\sqrt{7}+1\approx 3.645751311$$

$$x=1-\sqrt{7}\approx -1.645751311$$

Steps by Finding Square Root

Add 5 to both sides of the equation.

$$3\left(x-1\right)^{2}-5+5=16+5$$

Subtracting 5 from itself leaves 0.

$$3\left(x-1\right)^{2}=16+5$$

Add 16 to 5.

$$3\left(x-1\right)^{2}=21$$

Divide both sides by 3.

$$\frac{3\left(x-1\right)^{2}}{3}=\frac{21}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$\left(x-1\right)^{2}=\frac{21}{3}$$

Divide 21 by 3.

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

Take the square root of both sides of the equation.

$$x-1=\sqrt{7} x-1=-\sqrt{7}$$

Add 1 to both sides of the equation.

$$x-1-\left(-1\right)=\sqrt{7}-\left(-1\right) x-1-\left(-1\right)=-\sqrt{7}-\left(-1\right)$$

Subtracting -1 from itself leaves 0.

$$x=\sqrt{7}-\left(-1\right) x=-\sqrt{7}-\left(-1\right)$$

Subtract -1 from \sqrt{7}.

$$x=\sqrt{7}+1$$

Subtract -1 from -\sqrt{7}.

$$x=1-\sqrt{7}$$

The equation is now solved.

$$x=\sqrt{7}+1 x=1-\sqrt{7}$$