Chapter 11, Problem 17CCSR

To determine

Find the negative solution of the equation $2x^2+x=3$ .

Answer to Problem 17CCSR

Negative solution of the equation $2x^2+x=3$ is $x=-\frac{3}{2}$

Explanation of Solution

Given:

The equation: $2x^2+x=3$

Concept Used:

Zero-Product Property: If we multiply two (or more) things together and the result is equal to zero, then we know that  at least one  of those things that we multiplied must also have been equal to zero.

Calculation:

Rewrite the equation in standard form: $2x^2+x=3\Rightarrow 2x^2+x-3=0$

Find the factor form of the equation: $2x^2+x-3=0$

Factor form: $\begin{array}{l}2x^2+x-3=0\Rightarrow (2x+3)(x-1)=0\\ \end{array}$

Now use zero product property:

  $\begin{array}{l}2x^2+x-3=0\\ (2x+3)(x-1)=0\\ 2x+3=0\text{and}x-1=0[\text{Zero-Product Property}]\\ x=-\frac{3}{2}\text{and}x=1\end{array}$

Thus, the negative solution of the equation $2x^2+x=3$ is $x=-\frac{3}{2}$