Consider the following quadratic equation:
x^2+4x=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 + 4x = 6.
To find the number of solutions, we calculate the discriminant, which is given by the expression b^2 - 4ac.
Here, a = 1, b = 4, and c = -6.
Discriminant = (4)^2 - 4(1)(-6)
= 16 + 24
= 40
Since the discriminant is positive, there are two distinct real solutions to the quadratic equation.
Now, we can solve the quadratic equation using the formula x = (-b ± √(b^2 - 4ac)) / (2a).
x = (-4 ± √40) / (2)
= (-4 ± 2√10) / (2)
= -2 ± √10
Therefore, the solutions to the quadratic equation x^2 + 4x = 6 are x = -2 + √10 and x = -2 - √10.