Yes, sometimes factoring doesn't work. That's when we fall back on the quadratic formula.
4x^2 + 5x - 6 = 0
This is in the general form, y = ax^2 + bx + c. From that, we extract the values we need
when we use the quadratic formula.
-b ± sqrt(b^2 - 4ac)
x = --------------------------
2a
-5 ± sqrt(5^2 - 4(4)(-6))
x = -------------------------------
2(4)
-5 ± sqrt(25 + 96)
x = ------------------------
8
-5 ± sqrt(121)
x = --------------------
8
-5 ± 11
x = -----------
8
-5 + 11 -5 - 11
x = ----------- and x = -----------
8 8
6 -16
x = --- and x = ------
8 8
3
x = --- and x = -2
4
Always check your answers.
4x^2 + 5x = 6
4(3/4)^2 + 5(3/4) = 6
4(9/16) + 15/4 = 6
9/4 + 15/4 = 6
24/4 = 6
6 = 6 That one checks.
4x^2 + 5x = 6
4(-2)^2 + 5(-2) = 6
4(4) - 10 = 6
16 - 10 = 6
6 = 6 That one checks, too.
Answer: x = 3/4 and x = -2
The question was: solve for x in this quadratic equation: 4x^2 + 5x = 6
in this quadratic equation 4x^2 + 5x -6 = 0
how can I solve for x?
How does it go step by step. I tried factoring, but got stuck because nothing made sense
(2x + ) (2x - ) = 0