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

1 Answer
Alan P.
Jul 5, 2015

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

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