4y^2+16y-24=0

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Solution for 4y^2+16y-24=0 equation:


Simplifying
4y2 + 16y + -24 = 0

Reorder the terms:
-24 + 16y + 4y2 = 0

Solving
-24 + 16y + 4y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-6 + 4y + y2) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(-6 + 4y + y2)' equal to zero and attempt to solve: Simplifying -6 + 4y + y2 = 0 Solving -6 + 4y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + 4y + 6 + y2 = 0 + 6 Reorder the terms: -6 + 6 + 4y + y2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 4y + y2 = 0 + 6 4y + y2 = 0 + 6 Combine like terms: 0 + 6 = 6 4y + y2 = 6 The y term is 4y. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4y + 4 + y2 = 6 + 4 Reorder the terms: 4 + 4y + y2 = 6 + 4 Combine like terms: 6 + 4 = 10 4 + 4y + y2 = 10 Factor a perfect square on the left side: (y + 2)(y + 2) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (y + 2) equal to 3.16227766 and -3.16227766.

Subproblem 1

y + 2 = 3.16227766 Simplifying y + 2 = 3.16227766 Reorder the terms: 2 + y = 3.16227766 Solving 2 + y = 3.16227766 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + y = 3.16227766 + -2 Combine like terms: 2 + -2 = 0 0 + y = 3.16227766 + -2 y = 3.16227766 + -2 Combine like terms: 3.16227766 + -2 = 1.16227766 y = 1.16227766 Simplifying y = 1.16227766

Subproblem 2

y + 2 = -3.16227766 Simplifying y + 2 = -3.16227766 Reorder the terms: 2 + y = -3.16227766 Solving 2 + y = -3.16227766 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + y = -3.16227766 + -2 Combine like terms: 2 + -2 = 0 0 + y = -3.16227766 + -2 y = -3.16227766 + -2 Combine like terms: -3.16227766 + -2 = -5.16227766 y = -5.16227766 Simplifying y = -5.16227766

Solution

The solution to the problem is based on the solutions from the subproblems. y = {1.16227766, -5.16227766}

Solution

y = {1.16227766, -5.16227766}

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