Question

solve for x.
$5x^2 + 2 = -11x$
if there is more than one solution, separate them with commas.
if there is no solution, click on
o solution\.
x =
(there are some input buttons on the right side, including fraction, mixed number, no solution, multiple input, square root, reset, and close buttons.)

Explanation:

Step1: Rearrange the equation

First, we need to rewrite the quadratic equation in standard form \(ax^2 + bx + c = 0\). Starting with \(5x^2 + 2=-11x\), we add \(11x\) to both sides to get \(5x^2 + 11x + 2 = 0\).

Step2: Use the quadratic formula

The quadratic formula is \(x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\). For the equation \(5x^2 + 11x + 2 = 0\), we have \(a = 5\), \(b = 11\), and \(c = 2\). First, calculate the discriminant \(\Delta=b^2-4ac=(11)^2-4\times5\times2=121 - 40 = 81\). Then, find the roots: \(x=\frac{-11\pm\sqrt{81}}{2\times5}=\frac{-11\pm9}{10}\).

Step3: Calculate the two solutions

For the plus sign: \(x=\frac{-11 + 9}{10}=\frac{-2}{10}=-\frac{1}{5}\). For the minus sign: \(x=\frac{-11-9}{10}=\frac{-20}{10}=-2\).

Answer:

\(-2, -\frac{1}{5}\)