Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth.
x2 – 6 = x(1 point)
Responses
x = 2, 3
x = 2, 3
x = 2, –3
x = 2, –3
x = –2, –3
x = –2, –3
x = –2, 3
First, rearrange the equation to form a quadratic equation in standard form:
x2 - x - 6 = 0
Now, identify the coefficients of the quadratic equation, which are a, b, and c in the general form ax^2 + bx + c = 0:
a = 1
b = -1
c = -6
Now use the quadratic formula to find the values of x:
x = [-(-1) ± √((-1)^2 - 4(1)(-6))] / 2(1)
x = [1 ± √(1 + 24)] / 2
x = [1 ± √(25)] / 2
x = [1 ± 5] / 2
Now solve for x:
x = (1 + 5) / 2 = 6 / 2 = 3
x = (1 - 5) / 2 = -4 / 2 = -2
Therefore, the solutions to the equation using the quadratic formula are x = 3 and x = -2.