How do you solve x^2+4x= -1?

1 Answer
May 20, 2016

x = -2 \pm \sqrt{3}

Explanation:

There are several ways to do it, by I would prefer in this case to use the completing the square method to find the root of the quadratic x^2 + 4x = -1.

  • In completing the square, we need to first make sure whether the a value of the quadratic equation equals to 1. If not, then you need to divide every coefficient and constant by the a value to make sure that the a value is 1. In this case, this is not required.

  • Now we need to divide the b term by 2 and then square it. Do this to both sides.
    x^2 + 4x + (\frac{4}{2})^2 = -1 + (\frac{4}{2})^2
    x^2 + 4x + 4 = -1 + 4
    x^2 + 4x + 4 = 3

  • Put x^2 + 4x + 4 into a binomial.
    (x + 2)^2 = 3

  • To solve for x, find the square root of both sides.
    \sqrt{(x+2)^2} = \sqrt{3}
    x + 2 = \pm \sqrt{3}
    Notice the \pm in front of the square root of 3. This is because the square root of 3 can be both a positive and a negative (a negative times a negative is a positive).

  • Isolate x by subtracting 2 from both sides.
    x = -2 \pm \sqrt{3}

Answer: x = -2 \pm \sqrt{3}