Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth.
x^2-2=-3x
a
3.56, –0.56
b
–3.56, –0.56
c
3.56, 0.56
d
–3.56, 0.56
To solve the equation x^2 - 2 = -3x using the quadratic formula:
First, move all terms to one side of the equation to get: x^2 + 3x - 2 = 0
Next, identify the values of a, b, and c in the quadratic formula. In this equation, a = 1, b = 3, and c = -2.
Substitute these values into the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a)
x = (-(3) ± √((3)^2 - 4(1)(-2))) / (2(1))
Simplifying the equation inside the square root: x = (-3 ± √(9 + 8)) / 2
Simplifying further: x = (-3 ± √(17)) / 2
Calculating the square root of 17 and rounding to the nearest hundredth: √17 ≈ 4.12
x = (-3 + 4.12) / 2 ≈ 1.12 / 2 ≈ 0.56
x = (-3 - 4.12) / 2 ≈ -7.12 / 2 ≈ -3.56
Therefore, the solutions to the equation x^2 - 2 = -3x using the quadratic formula are approximately x = 0.56 and x = -3.56. Rounded to the nearest hundredth, the solutions are:
a) 3.56, -0.56