Question

solve for x.
$4x^2 + 9x = -2$
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 of the answer box, including fraction, mixed number, no solution, etc., and reset and close buttons at the bottom.)

Explanation:

Step1: Rewrite in standard form

First, we rewrite the quadratic equation \(4x^{2}+9x = - 2\) in standard form \(ax^{2}+bx + c=0\) by adding 2 to both sides. So we get \(4x^{2}+9x + 2=0\).

Step2: Use quadratic formula

The quadratic formula is \(x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}\). For the equation \(4x^{2}+9x + 2 = 0\), we have \(a = 4\), \(b=9\) and \(c = 2\).

First, calculate the discriminant \(\Delta=b^{2}-4ac\). Substitute the values: \(\Delta=9^{2}-4\times4\times2=81 - 32 = 49\).

Then, find the roots:
\(x=\frac{-9\pm\sqrt{49}}{2\times4}=\frac{-9\pm7}{8}\)

Step3: Calculate the two solutions

For the plus sign: \(x=\frac{-9 + 7}{8}=\frac{-2}{8}=-\frac{1}{4}\)

For the minus sign: \(x=\frac{-9-7}{8}=\frac{-16}{8}=- 2\)

Answer:

\(-2,-\frac{1}{4}\)