solve for y
x=(3-4y)^2
I've been stuck on this stupid question anyone? ._.
To solve for y in the equation x = (3 - 4y)², you can follow the steps below:
Step 1: Expand the equation:
x = (3 - 4y)²
x = (3 - 4y)(3 - 4y)
x = 9 - 12y + 16y²
Step 2: Rearrange the equation:
16y² - 12y + 9 - x = 0
Step 3: This quadratic equation can be solved using the quadratic formula:
The quadratic formula is given by: y = (-b ± √(b² - 4ac)) / (2a)
In this case, a = 16, b = -12, and c = 9 - x.
Step 4: Substitute these values into the quadratic formula:
y = (-(-12) ± √((-12)² - 4(16)(9 - x))) / (2 * 16)
y = (12 ± √(144 - 64(9 - x))) / 32
y = (12 ± √(144 - 576 + 64x)) / 32
y = (12 ± √(-432 + 64x)) / 32
Step 5: Simplify the square root if possible and divide to further simplify:
The result depends on the value inside the square root. If 144 - 576 + 64x < 0, then the equation has no solution.
If 144 - 576 + 64x ≥ 0, then we can simplify the square root as √(-432 + 64x) = √(64x - 432):
y = (12 ± √(64x - 432)) / 32
So, the value of y can be expressed as either (12 + √(64x - 432)) / 32 or (12 - √(64x - 432)) / 32, depending on the value inside the square root.