Q. 2 - Precalculus Enhanced with Graphing Utilities

Question

Find the real solutions of the equation $2x^2+7x-4=0$.

Step-by-Step Solution

Answer

The real solutions of the given equation are $-4$ and 0.5.

Step 1. Given information.

The given quadratic equation is:

$2x^2+7x-4=0$

Step 2. Solve the equation.

Spite the middle term and rewrite the given equation.

$\begin{array}{rcl}2x^2+8x-x-4& =& 0\\ 2x(x+4)-(x+4)& =& 0\\ (x+4)(2x-1)& =& 0\end{array}$

Use zero product property.

$\begin{array}{rcl}x+4& =& 0\text{ and }2x-1=0\\ x& =& -4\text{ and }x=\frac{1}{2}\\ x& =& -4\text{ and }x=0.5\end{array}$

Step 3. Conclusion.

The real solutions of the given equation are $-4$ and 0.5.