Question

solve the equation by factoring, using tables, or by graphing.
$5x^2 + 9x = 7$
$x = \square$
(simplify your answer. type an integer or a decimal rounded to the nearest hundredth as needed. use a comma to se

Explanation:

Step1: Rewrite in standard quadratic form

$5x^2 + 9x - 7 = 0$

Step2: Apply quadratic formula

For $ax^2+bx+c=0$, $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$. Here $a=5$, $b=9$, $c=-7$.
$$x=\frac{-9\pm\sqrt{9^2-4(5)(-7)}}{2(5)}$$

Step3: Calculate discriminant

$\sqrt{81 + 140}=\sqrt{221}\approx14.866$

Step4: Compute two solutions

$x_1=\frac{-9 + 14.866}{10}=\frac{5.866}{10}\approx0.59$
$x_2=\frac{-9 - 14.866}{10}=\frac{-23.866}{10}\approx-2.39$

Answer:

$0.59, -2.39$