Question

solve the quadratic equation.
x² + 4x = -5
write one exact, simplified solution in each box. you can add or remove boxes. if a solution is
not a real number, write it in the form a + bi or a - bi, where a and b are real numbers.

,

Explanation:

Step1: Rewrite in standard form

First, rewrite the quadratic equation \(x^{2}+4x = - 5\) in standard form \(ax^{2}+bx + c=0\) by adding 5 to both sides:
\(x^{2}+4x + 5=0\)

Step2: Use quadratic formula

The quadratic formula for a quadratic equation \(ax^{2}+bx + c = 0\) is \(x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}\). For the equation \(x^{2}+4x + 5=0\), we have \(a = 1\), \(b=4\), and \(c = 5\).

First, calculate the discriminant \(\Delta=b^{2}-4ac\):
\(\Delta=(4)^{2}-4\times1\times5=16 - 20=- 4\)

Then, substitute \(a\), \(b\), and \(\Delta\) into the quadratic formula:
\(x=\frac{-4\pm\sqrt{-4}}{2\times1}=\frac{-4\pm2i}{2}\) (since \(\sqrt{-4}=\sqrt{4}\times\sqrt{-1} = 2i\))

Simplify the fraction:
\(x=-2\pm i\)

Answer:

\(-2 + i\), \(-2 - i\)