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Simplifying 3y2(4y2 + 5y + -4) = 0 Reorder the terms: 3y2(-4 + 5y + 4y2) = 0 (-4 * 3y2 + 5y * 3y2 + 4y2 * 3y2) = 0 (-12y2 + 15y3 + 12y4) = 0 Solving -12y2 + 15y3 + 12y4 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '3y2'. 3y2(-4 + 5y + 4y2) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'y2' equal to zero and attempt to solve: Simplifying y2 = 0 Solving y2 = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y2 = 0 Take the square root of each side: y = {0}Subproblem 2
Set the factor '(-4 + 5y + 4y2)' equal to zero and attempt to solve: Simplifying -4 + 5y + 4y2 = 0 Solving -4 + 5y + 4y2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1 + 1.25y + y2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 1.25y + 1 + y2 = 0 + 1 Reorder the terms: -1 + 1 + 1.25y + y2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 1.25y + y2 = 0 + 1 1.25y + y2 = 0 + 1 Combine like terms: 0 + 1 = 1 1.25y + y2 = 1 The y term is 1.25y. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25y + 0.390625 + y2 = 1 + 0.390625 Reorder the terms: 0.390625 + 1.25y + y2 = 1 + 0.390625 Combine like terms: 1 + 0.390625 = 1.390625 0.390625 + 1.25y + y2 = 1.390625 Factor a perfect square on the left side: (y + 0.625)(y + 0.625) = 1.390625 Calculate the square root of the right side: 1.179247642 Break this problem into two subproblems by setting (y + 0.625) equal to 1.179247642 and -1.179247642.Subproblem 1
y + 0.625 = 1.179247642 Simplifying y + 0.625 = 1.179247642 Reorder the terms: 0.625 + y = 1.179247642 Solving 0.625 + y = 1.179247642 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + y = 1.179247642 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + y = 1.179247642 + -0.625 y = 1.179247642 + -0.625 Combine like terms: 1.179247642 + -0.625 = 0.554247642 y = 0.554247642 Simplifying y = 0.554247642Subproblem 2
y + 0.625 = -1.179247642 Simplifying y + 0.625 = -1.179247642 Reorder the terms: 0.625 + y = -1.179247642 Solving 0.625 + y = -1.179247642 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + y = -1.179247642 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + y = -1.179247642 + -0.625 y = -1.179247642 + -0.625 Combine like terms: -1.179247642 + -0.625 = -1.804247642 y = -1.804247642 Simplifying y = -1.804247642Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.554247642, -1.804247642}Solution
y = {0, 0.554247642, -1.804247642}
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