Solve (m-2)^2+16=45

$$( m - 2 ) ^ { 2 } + 16 = 45$$

Solve for m

$$m=\sqrt{29}+2\approx 7.385164807$$

$$m=2-\sqrt{29}\approx -3.385164807$$

Steps by Finding Square Root

Subtract 16 from both sides of the equation.

$$\left(m-2\right)^{2}+16-16=45-16$$

Subtracting 16 from itself leaves 0.

$$\left(m-2\right)^{2}=45-16$$

Subtract 16 from 45.

$$\left(m-2\right)^{2}=29$$

Take the square root of both sides of the equation.

$$m-2=\sqrt{29} m-2=-\sqrt{29}$$

Add 2 to both sides of the equation.

$$m-2-\left(-2\right)=\sqrt{29}-\left(-2\right) m-2-\left(-2\right)=-\sqrt{29}-\left(-2\right)$$

Subtracting -2 from itself leaves 0.

$$m=\sqrt{29}-\left(-2\right) m=-\sqrt{29}-\left(-2\right)$$

Subtract -2 from \sqrt{29}.

$$m=\sqrt{29}+2$$

Subtract -2 from -\sqrt{29}.

$$m=2-\sqrt{29}$$

The equation is now solved.

$$m=\sqrt{29}+2 m=2-\sqrt{29}$$