Solve (x-4)^2-17=0

$$( x - 4 ) ^ { 2 } - 17 = 0$$

Solve for x

$$x=\sqrt{17}+4\approx 8.123105626$$

$$x=4-\sqrt{17}\approx -0.123105626$$

Steps by Finding Square Root

Add 17 to both sides of the equation.

$$\left(x-4\right)^{2}-17+17=17$$

Subtracting 17 from itself leaves 0.

$$\left(x-4\right)^{2}=17$$

Take the square root of both sides of the equation.

$$x-4=\sqrt{17} x-4=-\sqrt{17}$$

Add 4 to both sides of the equation.

$$x-4-\left(-4\right)=\sqrt{17}-\left(-4\right) x-4-\left(-4\right)=-\sqrt{17}-\left(-4\right)$$

Subtracting -4 from itself leaves 0.

$$x=\sqrt{17}-\left(-4\right) x=-\sqrt{17}-\left(-4\right)$$

Subtract -4 from \sqrt{17}.

$$x=\sqrt{17}+4$$

Subtract -4 from -\sqrt{17}.

$$x=4-\sqrt{17}$$

The equation is now solved.

$$x=\sqrt{17}+4 x=4-\sqrt{17}$$