Question

Solve each equation by factoring or by using the quadratic formula. The quadratic formula is:

If$a{x}^2+bx+c=0$, with$a\ne 0$, then$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$.

$x^2+3x-2=0$

Short answer

The values of x are$x=\frac{-3+\sqrt{17}}{2}$ and$x=\frac{-3-\sqrt{17}}{2}$.

Step-by-step solution

- Understand the concept used 

If$a{x}^2+bx+c=0$ , with$a\ne 0$, then$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ . Solving using factoring can be done by splitting the middle term of equation and then making groups and equating them to zero.

- Substitute the values 

It is given that$x^2+3x-2=0$.Using quadratic formula$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$, substitute 1 for a, 3 for b and -2 for c.

Put the values in the formula and get$x=\frac{-3\pm \sqrt{{\left(3\right)}^2-4\times \left(1\right)\times \left(-2\right)}}{2\left(1\right)}$.

- Simplify for x 

Simplify the expression for x.

$\begin{array}{c}x=\frac{-3\pm \sqrt{{\left(3\right)}^2-4\times \left(1\right)\times \left(-2\right)}}{2\left(1\right)}\\ =\frac{-3\pm \sqrt{9+8}}{2}\\ =\frac{-3\pm \sqrt{17}}{2}\end{array}$

Therefore,$x=\frac{-3+\sqrt{17}}{2}$ and $x=\frac{-3-\sqrt{17}}{2}$.