Question

solve for x.
$4x^2 + 9 = -12x$
if there is more than one solution, separate them with commas.
if there is no solution, click on
o solution\.
$x = \square$

Explanation:

Step1: Rearrange the equation to standard quadratic form.

Start with the given equation \(4x^{2}+9 = - 12x\). Add \(12x\) to both sides to get \(4x^{2}+12x + 9=0\).

Step2: Factor the quadratic equation.

Notice that \(4x^{2}+12x + 9\) is a perfect square trinomial. We know that \((ax + b)^{2}=a^{2}x^{2}+2abx + b^{2}\). Here, \(a = 2\) (since \(a^{2}=4\)) and \(b = 3\) (since \(b^{2}=9\) and \(2ab=2\times2\times3 = 12\)). So, \(4x^{2}+12x + 9=(2x + 3)^{2}\). The equation becomes \((2x + 3)^{2}=0\).

Step3: Solve for \(x\).

Take the square root of both sides: \(2x+3 = 0\). Subtract 3 from both sides: \(2x=-3\). Divide both sides by 2: \(x=-\frac{3}{2}\).

Answer:

\(-\frac{3}{2}\)