Question

solve the equation by factoring, using tables, or by graphing
$5x^2 + 8x = 7$
$x = \square$
(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

$5x^2 + 8x - 7 = 0$

Step2: Identify coefficients

$a=5$, $b=8$, $c=-7$

Step3: Apply quadratic formula

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

Step4: Calculate discriminant

$\sqrt{8^2 - 4(5)(-7)} = \sqrt{64 + 140} = \sqrt{204} \approx 14.28$

Step5: Compute two roots

$x_1 = \frac{-8 + 14.28}{10} \approx 0.64$
$x_2 = \frac{-8 - 14.28}{10} \approx -2.24$

Answer:

0.64, -2.24