Solve x^2-17=104

$$x ^ { 2 } - 17 = 104$$

Solve for x

$$x=11$$

$$x=-11$$

Steps Using Difference of Squares

Subtract 104 from both sides.

$$x^{2}-17-104=0$$

Subtract 104 from -17 to get -121.

$$x^{2}-121=0$$

Consider x^{2}-121. Rewrite x^{2}-121 as x^{2}-11^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-11\right)\left(x+11\right)=0$$

To find equation solutions, solve x-11=0 and x+11=0.

$$x=11 x=-11$$

Steps by Finding Square Root

Add 17 to both sides.

$$x^{2}=104+17$$

Add 104 and 17 to get 121.

$$x^{2}=121$$

Take the square root of both sides of the equation.

$$x=11 x=-11$$

Steps Using the Quadratic Formula

Subtract 104 from both sides.

$$x^{2}-17-104=0$$

Subtract 104 from -17 to get -121.

$$x^{2}-121=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -121 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-121\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-121\right)}}{2}$$

Multiply -4 times -121.

$$x=\frac{0±\sqrt{484}}{2}$$

Take the square root of 484.

$$x=\frac{0±22}{2}$$

Now solve the equation x=\frac{0±22}{2} when ± is plus. Divide 22 by 2.

$$x=11$$

Now solve the equation x=\frac{0±22}{2} when ± is minus. Divide -22 by 2.

$$x=-11$$

The equation is now solved.

$$x=11 x=-11$$