SOLUTION: Solve for x: x^2 + 7x + 4 = 0. If the solutions are complex numbers, then give your solutions in the usual a + bi form.

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Solve for x: x^2 + 7x + 4 = 0. If the solutions are complex numbers, then give your solutions in the usual a + bi form.       Log On


   



Question 189423: Solve for x: x^2 + 7x + 4 = 0. If the solutions are complex numbers, then give your solutions in the usual a + bi form.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2+%2B+7x+%2B+4+=+0
Subtract 4 from both sides
x%5E2+%2B+7x+=+-4
Complete the square by taking 1%2F2 of the
coefficient of the x term, square it, and
add it to both sides
x%5E2+%2B+7x+%2B+%287%2F2%29%5E2+=+-4+%2B+%287%2F2%29%5E2
x%5E2+%2B+7x+%2B+49%2F4+=+-4+%2B+49%2F4
x%5E2+%2B+7x+%2B+49%2F4+=+-%2816%2F4%29+%2B+49%2F4
x%5E2+%2B+7x+%2B+49%2F4+=+33%2F4
The left side is a perfect square. Rewrite it.
%28x+%2B+7%2F2%29%5E2+=+33%2F4
Take the square root of both sides
x+%2B+7%2F2+=+sqrt%2833%29%2F2
and also
x+%2B+7%2F2+=+-sqrt%2833%29%2F2
so
x+=+%28-7+%2B+sqrt%2833%29%29%2F2
and
x+=+%28-7+-+sqrt%2833%29%29%2F2