Question

Solve the quadratic equations below. Use any method you want.

$x(x+3)+12=0$

Short answer

There is no real solution because the square root of the negative number -39 is not real.

As a result, the equation has no solution.

Step-by-step solution

Given information.

The given equation is

$x(x+3)+12=0$

Step 2. Use the quadratic formula to solve the equation.

First, write the equation $a{x}^2+bx+c=0$ a in standard form, as shown below.

[Use distributive property]

$$\begin{gathered} x·x+3·x+12=0 \\ {x}^2+3x+12=0 \end{gathered}$$

In standard form, the equation is

$x^2+3x+12=0$

Determine the a, b, and c values.

In comparison to the standard form, the values are a=1,b=3, and c=12.

In the quadratic formula, substitute a=1, b=3, and c= -12.

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

Put the value.

localid="1653830429546" $x=\frac{-3\pm \sqrt{{\left(3\right)}^2-4\left(1\right)(-12)}}{2\left(1\right)}$

As shown below, simplify the fraction.

$$\begin{gathered} x=\frac{-3\pm \sqrt{9-48}}{2} \\ x=\frac{-3\pm \sqrt{-39}}{2} \end{gathered}$$

There is no real solution because the square root of the negative number -39 is not real.

As a result, the equation has no solution.