Chapter 3.3, Problem 2AYU

To determine

To calculate: The solutions of the given quadratic equation $2x^2+7x-4=0$.

Answer to Problem 2AYU

The solutions of the given equations are $x=-4$ and $x=\frac{1}{2}$.

Explanation of Solution

Given:

The given equation is

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

Formula used:

A quadratic equation of the form $a{x}^2+bx+c=0$ can be solved using the quadratic formula.

Therefore, we get the solution as

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Calculation:

Using the quadratic formula, we can find the solution to the given equation as

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

$\Rightarrow x=\frac{-7\pm \sqrt{7^2-4(2)(-4)}}{2(2)}$

$\Rightarrow x=\frac{-7\pm \sqrt{49+32}}{4}$

$\Rightarrow x=\frac{-7\pm \sqrt{81}}{4}$

$\Rightarrow x=\frac{-7\pm 9}{4}$

Therefore, we can see that there are 2 solutions to the given equation.

$\begin{array}{l}x=\frac{-7+9}{4}\\ \Rightarrow x=\frac{1}{2}\end{array}$

And

$\begin{array}{l}x=\frac{-7-9}{4}\\ \Rightarrow x=-4\end{array}$

Thus, the solutions of the given equations are $x=-4$ and $x=\frac{1}{2}$