Question

solve the equation by factoring, using tables, or by graphing.
$4x^2 + 7x = 8$
$x = \square$
(simplify your answer. type an integer or a decimal rounded to the nearest hundredth as needed. use a comma to separate answers as needed.)

Explanation:

Step1: Rewrite to standard quadratic form

$4x^2 + 7x - 8 = 0$

Step2: Apply quadratic formula

For $ax^2+bx+c=0$, $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$. Here $a=4$, $b=7$, $c=-8$.
$$x=\frac{-7\pm\sqrt{7^2-4(4)(-8)}}{2(4)}$$

Step3: Calculate discriminant

$\sqrt{49 + 128}=\sqrt{177}\approx13.3041$

Step4: Compute two solutions

$x_1=\frac{-7 + 13.3041}{8}\approx\frac{6.3041}{8}\approx0.79$
$x_2=\frac{-7 - 13.3041}{8}\approx\frac{-20.3041}{8}\approx-2.54$

Answer:

0.79, -2.54