Question

Solve x^2 + 4x + 8 = 0.

Answer 1

Since −8 does not contain the variable to solve for, move it to the right side of the equation by adding 8 to both sides. To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of b , the coefficient of x . Add the term to each side of the equation.

Answer 2

Answer:

The solution to the quadratic equations are:

$x=-2+2i,\:x=-2-2i$

Step-by-step explanation:

Consider the provided quadratic equation.

$x^2 + 4x + 8 = 0$

$\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Substitute a=1, b=4 and c=8 in above formula.

$x_{1,\:2}=\frac{-4\pm \sqrt{4^2-4\cdot \:1\cdot \:8}}{2\cdot \:1}$

$x_{1,\:2}=\frac{-4\pm \sqrt{16-32}}{2}$

$x_{1,\:2}=\frac{-4\pm \sqrt{-16}}{2}$

$x_{1,\:2}=\frac{-4\pm 4i}{2}$

$x_{1,\:2}=-2\pm 2i$

Hence, the solution to the quadratic equations are:

$x=-2+2i,\:x=-2-2i$