Solve n^2-17-50=-8

$$n ^ { 2 } - 17 - 50 = - 8$$

Solve for n

$$n=\sqrt{59}\approx 7.681145748$$

$$n=-\sqrt{59}\approx -7.681145748$$

Steps by Finding Square Root

Subtract 50 from -17 to get -67.

$$n^{2}-67=-8$$

Add 67 to both sides.

$$n^{2}=-8+67$$

Add -8 and 67 to get 59.

$$n^{2}=59$$

Take the square root of both sides of the equation.

$$n=\sqrt{59} n=-\sqrt{59}$$

Steps Using the Quadratic Formula

Subtract 50 from -17 to get -67.

$$n^{2}-67=-8$$

Add 8 to both sides.

$$n^{2}-67+8=0$$

Add -67 and 8 to get -59.

$$n^{2}-59=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -59 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$n=\frac{0±\sqrt{0^{2}-4\left(-59\right)}}{2}$$

Square 0.

$$n=\frac{0±\sqrt{-4\left(-59\right)}}{2}$$

Multiply -4 times -59.

$$n=\frac{0±\sqrt{236}}{2}$$

Take the square root of 236.

$$n=\frac{0±2\sqrt{59}}{2}$$

Now solve the equation n=\frac{0±2\sqrt{59}}{2} when ± is plus.

$$n=\sqrt{59}$$

Now solve the equation n=\frac{0±2\sqrt{59}}{2} when ± is minus.

$$n=-\sqrt{59}$$

The equation is now solved.

$$n=\sqrt{59} n=-\sqrt{59}$$