Question

e quadratic by factoring.
$x^2 + 9x + 20 = -3x$
er attempt 1 out of 10

Explanation:

Step1: Move all terms to left side

To solve the quadratic equation \(x^{2}+9x + 20=-3x\), we first move all terms to the left - hand side. Add \(3x\) to both sides of the equation:
\(x^{2}+9x + 3x+20 = 0\)
Simplify the like terms (\(9x+3x = 12x\)):
\(x^{2}+12x + 20=0\)

Step2: Factor the quadratic

We need to factor the quadratic expression \(x^{2}+12x + 20\). We look for two numbers that multiply to \(20\) (the constant term) and add up to \(12\) (the coefficient of the \(x\) term). The numbers are \(10\) and \(2\) since \(10\times2 = 20\) and \(10 + 2=12\).
So we can factor \(x^{2}+12x + 20\) as \((x + 10)(x+2)=0\)

Step3: Solve for x

Using the zero - product property, if \(ab = 0\), then either \(a = 0\) or \(b = 0\).
For \((x + 10)(x + 2)=0\), we set each factor equal to zero:

• If \(x+10 = 0\), then \(x=-10\)
• If \(x + 2=0\), then \(x=-2\)

Answer:

\(x=-10\) or \(x = - 2\)