Solve {c}{x^2+(m+1)x+1/2=0}{x=-1}

$$\left. \begin{array} { c } { x ^ { 2 } + ( m + 1 ) x + \frac { 1 } { 2 } = 0 } \\ { x = - 1 } \end{array} \right.$$

Solve for x, m

$$x=-1$$

$$m=\frac{1}{2}=0.5$$

Solution Steps

Consider the first equation. Insert the known values of variables into the equation.

$$\left(-1\right)^{2}+\left(m+1\right)\left(-1\right)+\frac{1}{2}=0$$

Calculate -1 to the power of 2 and get 1.

$$1+\left(m+1\right)\left(-1\right)+\frac{1}{2}=0$$

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

$$1-m-1+\frac{1}{2}=0$$

Subtract 1 from 1 to get 0.

$$-m+\frac{1}{2}=0$$

Subtract \frac{1}{2} from both sides. Anything subtracted from zero gives its negation.

$$-m=-\frac{1}{2}$$

Divide both sides by -1.

$$m=\frac{-\frac{1}{2}}{-1}$$

Express \frac{-\frac{1}{2}}{-1} as a single fraction.

$$m=\frac{-1}{2\left(-1\right)}$$

Cancel out -1 in both numerator and denominator.

$$m=\frac{1}{2}$$

The system is now solved.

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