use the quadratic formula to solve the equation 2x^2-3x=-6
2x^2 - 3x + 6 = 0.
x = 3+- sqrt(9 - 48) / 4 =
3 +- sqrt(-39) / 4 =
(3 +- sqrt(39*-1)) / 4
sqrt(-1) = i
x = +- isqrt(39) / 4
Solution Set:
x =(3 - isqrt(39)) / 4
x =(3 + isqrt(39)) / 4
To solve the equation 2x^2 - 3x = -6 using the quadratic formula, we can follow these steps:
Step 1: Rewrite the given equation in the standard quadratic form: ax^2 + bx + c = 0. In this case, the equation is already in standard form: 2x^2 - 3x + 6 = 0.
Step 2: Identify the values of a, b, and c. In the given equation, a = 2, b = -3, and c = 6.
Step 3: Plug the values of a, b, and c into the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a).
Step 4: Substitute the identified values into the quadratic formula: x = (-(−3) ± √((-3)^2 - 4(2)(6))) / (2(2)).
Step 5: Simplify the expression within the square root: x = (3 ± √(9 - 48)) / 4.
Step 6: Simplify further: x = (3 ± √(-39)) / 4.
Since the expression inside the square root is negative, the equation has no real solutions. The roots would be imaginary.