Question

How do you solve `x^2+7x=-3` using the quadratic formula?

Answer 1

Rewrite the given formula in standard form, then apply the quadratic formula for roots to get `x=-1/2` or `x=-13/2`

Explanation:

`x^2+7x=-3`
`color(white)("XXXX")`is equivalent to
`x^2+7x+3=0`
`color(white)("XXXX")`which is a quadratic in standard form
`color(white)("XXXX")` `color(white)("XXXX")` `ax^2+bx+c=0`
`color(white)("XXXX")`whose roots are given by the quadratic formula:
`color(white)("XXXX")` `color(white)("XXXX")` `x = (-b+-sqrt(b^2-4ac))/(2a)`

Using `a=1`, `b=7`, and `c=3`
we have
`color(white)("XXXX")` `x= (-7+-sqrt(7^2-4(1)(3)))/(2(1)`

`color(white)("XXXX")` `x = (-7+-sqrt(36))/2`

`color(white)("XXXX")` `x = (-7+-6)/2`

`x=-1/2` or `x=-13/2`