Solve 5x^2+17x=12x

$$5 x ^ { 2 } + 17 x = 12 x$$

Solve for x

$$x=-1$$

$$x=0$$

Steps Using the Quadratic Formula

Subtract 12x from both sides.

$$5x^{2}+17x-12x=0$$

Combine 17x and -12x to get 5x.

$$5x^{2}+5x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 5 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-5±\sqrt{5^{2}}}{2\times 5}$$

Take the square root of 5^{2}.

$$x=\frac{-5±5}{2\times 5}$$

Multiply 2 times 5.

$$x=\frac{-5±5}{10}$$

Now solve the equation x=\frac{-5±5}{10} when ± is plus. Add -5 to 5.

$$x=\frac{0}{10}$$

Divide 0 by 10.

$$x=0$$

Now solve the equation x=\frac{-5±5}{10} when ± is minus. Subtract 5 from -5.

$$x=-\frac{10}{10}$$

Divide -10 by 10.

$$x=-1$$

The equation is now solved.

$$x=0 x=-1$$

Steps for Completing the Square

Subtract 12x from both sides.

$$5x^{2}+17x-12x=0$$

Combine 17x and -12x to get 5x.

$$5x^{2}+5x=0$$

Divide both sides by 5.

$$\frac{5x^{2}+5x}{5}=\frac{0}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$x^{2}+\frac{5}{5}x=\frac{0}{5}$$

Divide 5 by 5.

$$x^{2}+x=\frac{0}{5}$$

Divide 0 by 5.

$$x^{2}+x=0$$

Divide 1, the coefficient of the x term, by 2 to get \frac{1}{2}. Then add the square of \frac{1}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+x+\left(\frac{1}{2}\right)^{2}=\left(\frac{1}{2}\right)^{2}$$

Square \frac{1}{2} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+x+\frac{1}{4}=\frac{1}{4}$$

Factor x^{2}+x+\frac{1}{4}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{1}{2}\right)^{2}=\frac{1}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{1}{2}\right)^{2}}=\sqrt{\frac{1}{4}}$$

Simplify.

$$x+\frac{1}{2}=\frac{1}{2} x+\frac{1}{2}=-\frac{1}{2}$$

Subtract \frac{1}{2} from both sides of the equation.

$$x=0 x=-1$$