Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth.%0D%0A%0D%0Ax^2 + 3 = –4x%0D%0A(1 point)

Answer 1

To solve the equation x^2 + 3 = -4x using the quadratic formula, first rewrite the equation in standard form:

x^2 + 4x + 3 = 0

Now identify a, b, and c in the standard form equation:

a = 1
b = 4
c = 3

Substitute the values of a, b, and c into the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

x = (-(4) ± √((4)^2 - 4(1)(3))) / 2(1)

x = (-4 ± √(16 - 12)) / 2

x = (-4 ± √4) / 2

Now calculate the two possible values of x:

x = (-4 + 2) / 2 = -2 / 2 = -1

x = (-4 - 2) / 2 = -6 / 2 = -3

Therefore, the solutions to the equation x^2 + 3 = -4x are x = -1 and x = -3.