Solve 2m+1/2*m=18

$$\frac { 2 m + 1 } { 2 } \times m = 18$$

Solve for m

$$m=4$$

$$m = -\frac{9}{2} = -4\frac{1}{2} = -4.5$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 2.

$$\left(2m+1\right)m=36$$

Use the distributive property to multiply 2m+1 by m.

$$2m^{2}+m=36$$

Subtract 36 from both sides.

$$2m^{2}+m-36=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 1 for b, and -36 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{-1±\sqrt{1^{2}-4\times 2\left(-36\right)}}{2\times 2}$$

Square 1.

$$m=\frac{-1±\sqrt{1-4\times 2\left(-36\right)}}{2\times 2}$$

Multiply -4 times 2.

$$m=\frac{-1±\sqrt{1-8\left(-36\right)}}{2\times 2}$$

Multiply -8 times -36.

$$m=\frac{-1±\sqrt{1+288}}{2\times 2}$$

Add 1 to 288.

$$m=\frac{-1±\sqrt{289}}{2\times 2}$$

Take the square root of 289.

$$m=\frac{-1±17}{2\times 2}$$

Multiply 2 times 2.

$$m=\frac{-1±17}{4}$$

Now solve the equation m=\frac{-1±17}{4} when ± is plus. Add -1 to 17.

$$m=\frac{16}{4}$$

Divide 16 by 4.

$$m=4$$

Now solve the equation m=\frac{-1±17}{4} when ± is minus. Subtract 17 from -1.

$$m=-\frac{18}{4}$$

Reduce the fraction \frac{-18}{4} to lowest terms by extracting and canceling out 2.

$$m=-\frac{9}{2}$$

The equation is now solved.

$$m=4 m=-\frac{9}{2}$$

Steps for Completing the Square

Multiply both sides of the equation by 2.

$$\left(2m+1\right)m=36$$

Use the distributive property to multiply 2m+1 by m.

$$2m^{2}+m=36$$

Divide both sides by 2.

$$\frac{2m^{2}+m}{2}=\frac{36}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$m^{2}+\frac{1}{2}m=\frac{36}{2}$$

Divide 36 by 2.

$$m^{2}+\frac{1}{2}m=18$$

Divide \frac{1}{2}, the coefficient of the x term, by 2 to get \frac{1}{4}. Then add the square of \frac{1}{4} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$m^{2}+\frac{1}{2}m+\left(\frac{1}{4}\right)^{2}=18+\left(\frac{1}{4}\right)^{2}$$

Square \frac{1}{4} by squaring both the numerator and the denominator of the fraction.

$$m^{2}+\frac{1}{2}m+\frac{1}{16}=18+\frac{1}{16}$$

Add 18 to \frac{1}{16}.

$$m^{2}+\frac{1}{2}m+\frac{1}{16}=\frac{289}{16}$$

Factor m^{2}+\frac{1}{2}m+\frac{1}{16}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(m+\frac{1}{4}\right)^{2}=\frac{289}{16}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(m+\frac{1}{4}\right)^{2}}=\sqrt{\frac{289}{16}}$$

Simplify.

$$m+\frac{1}{4}=\frac{17}{4} m+\frac{1}{4}=-\frac{17}{4}$$

Subtract \frac{1}{4} from both sides of the equation.

$$m=4 m=-\frac{9}{2}$$