Consider the following quadratic equation:
x^2+6x=−6
Step 2 of 2 : Use the discriminant, b2−4ac
, to determine the number of solutions of the given quadratic equation. Then solve the quadratic equation using the formula x=−b±b2−4ac⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯/2a
.
The given quadratic equation is x^2 + 6x = -6.
To use the discriminant to determine the number of solutions, we need to identify the values of a, b, and c in the quadratic equation of the form ax^2 + bx + c = 0.
Here, a = 1, b = 6, and c = -6.
Now, let's calculate the discriminant using the formula Δ = b^2 - 4ac:
Δ = (6)^2 - 4(1)(-6)
= 36 + 24
= 60
The discriminant Δ is positive and greater than 0, which means there are two distinct real solutions to the quadratic equation.
Now, let's solve the quadratic equation using the formula x = (-b ± √Δ) / (2a):
x = (-6 ± √60) / (2*1)
= (-6 ± √60) / 2
= -3 ± (√15/2)
Therefore, the solutions to the quadratic equation x^2 + 6x = -6 are:
x = -3 + (√15/2)
x = -3 - (√15/2)