Solve x^2-14=5x+67-5x

$$x ^ { 2 } - 14 = 5 x + 67 - 5 x$$

Solve for x

$$x=9$$

$$x=-9$$

Steps Using Difference of Squares

Combine 5x and -5x to get 0.

$$x^{2}-14=67$$

Subtract 67 from both sides.

$$x^{2}-14-67=0$$

Subtract 67 from -14 to get -81.

$$x^{2}-81=0$$

Consider x^{2}-81. Rewrite x^{2}-81 as x^{2}-9^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-9\right)\left(x+9\right)=0$$

To find equation solutions, solve x-9=0 and x+9=0.

$$x=9 x=-9$$

Steps by Finding Square Root

Combine 5x and -5x to get 0.

$$x^{2}-14=67$$

Add 14 to both sides.

$$x^{2}=67+14$$

Add 67 and 14 to get 81.

$$x^{2}=81$$

Take the square root of both sides of the equation.

$$x=9 x=-9$$

Steps Using the Quadratic Formula

Combine 5x and -5x to get 0.

$$x^{2}-14=67$$

Subtract 67 from both sides.

$$x^{2}-14-67=0$$

Subtract 67 from -14 to get -81.

$$x^{2}-81=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -81 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-81\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-81\right)}}{2}$$

Multiply -4 times -81.

$$x=\frac{0±\sqrt{324}}{2}$$

Take the square root of 324.

$$x=\frac{0±18}{2}$$

Now solve the equation x=\frac{0±18}{2} when ± is plus. Divide 18 by 2.

$$x=9$$

Now solve the equation x=\frac{0±18}{2} when ± is minus. Divide -18 by 2.

$$x=-9$$

The equation is now solved.

$$x=9 x=-9$$