Question

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

Answer 1

`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}`