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

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

Solve for x

$$x=\sqrt{19}+5\approx 9.358898944$$

$$x=5-\sqrt{19}\approx 0.641101056$$

Steps by Finding Square Root

Add 16 to both sides of the equation.

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

Subtracting 16 from itself leaves 0.

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

Add 3 to 16.

$$\left(x-5\right)^{2}=19$$

Take the square root of both sides of the equation.

$$x-5=\sqrt{19} x-5=-\sqrt{19}$$

Add 5 to both sides of the equation.

$$x-5-\left(-5\right)=\sqrt{19}-\left(-5\right) x-5-\left(-5\right)=-\sqrt{19}-\left(-5\right)$$

Subtracting -5 from itself leaves 0.

$$x=\sqrt{19}-\left(-5\right) x=-\sqrt{19}-\left(-5\right)$$

Subtract -5 from \sqrt{19}.

$$x=\sqrt{19}+5$$

Subtract -5 from -\sqrt{19}.

$$x=5-\sqrt{19}$$

The equation is now solved.

$$x=\sqrt{19}+5 x=5-\sqrt{19}$$