Solve.
9x^2 + 12x = 32
x2 + (4/3)x - (32/9) = 0
has two solutions:
x = -2/3 + √ 4
or
x = -2/3 - √ 4
This is the solution I came up with. Is this right?? Please and Thank you.
9x^2 +12x -32 0
(3x + 8) (3x -4) =0
3x + 8 = 0
3x - 4 = 0
x = -8/3
x = 4/3
To solve the equation 9x^2 + 12x = 32, we can follow these steps:
Step 1: Rewrite the equation in the form ax^2 + bx + c = 0.
9x^2 + 12x - 32 = 0
Step 2: Factor the quadratic equation if possible. In this case, factoring might not be straightforward, so we can move to the next step.
Step 3: Use the quadratic formula to find the solutions.
The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a)
Here, a = 9, b = 12, and c = -32.
Plugging these values into the quadratic formula, we have:
x = (-12 ± √(12^2 - 4 * 9 * -32)) / (2 * 9)
Simplifying further:
x = (-12 ± √(144 + 1152)) / 18
x = (-12 ± √(1296)) / 18
x = (-12 ± 36) / 18
Step 4: Simplify the solutions by dividing the numerator and denominator by their greatest common divisor (GCD).
x = (-12 ± 36) / 18
x = 24/18 or -48/18
Step 5: Reduce the fractions if possible.
x = 4/3 or -8/3
Hence, there are two solutions for the equation 9x^2 + 12x = 32: x = 4/3 or x = -8/3.
The solution you came up with, x = -2/3 + √4 or x = -2/3 - √4, seems to be incorrect.