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Simplifying -2y2 + -200y + 3200 = 0 Reorder the terms: 3200 + -200y + -2y2 = 0 Solving 3200 + -200y + -2y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(1600 + -100y + -1y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1600 + -100y + -1y2)' equal to zero and attempt to solve: Simplifying 1600 + -100y + -1y2 = 0 Solving 1600 + -100y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1600 + 100y + y2 = 0 Move the constant term to the right: Add '1600' to each side of the equation. -1600 + 100y + 1600 + y2 = 0 + 1600 Reorder the terms: -1600 + 1600 + 100y + y2 = 0 + 1600 Combine like terms: -1600 + 1600 = 0 0 + 100y + y2 = 0 + 1600 100y + y2 = 0 + 1600 Combine like terms: 0 + 1600 = 1600 100y + y2 = 1600 The y term is 100y. Take half its coefficient (50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. 100y + 2500 + y2 = 1600 + 2500 Reorder the terms: 2500 + 100y + y2 = 1600 + 2500 Combine like terms: 1600 + 2500 = 4100 2500 + 100y + y2 = 4100 Factor a perfect square on the left side: (y + 50)(y + 50) = 4100 Calculate the square root of the right side: 64.031242374 Break this problem into two subproblems by setting (y + 50) equal to 64.031242374 and -64.031242374.Subproblem 1
y + 50 = 64.031242374 Simplifying y + 50 = 64.031242374 Reorder the terms: 50 + y = 64.031242374 Solving 50 + y = 64.031242374 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + y = 64.031242374 + -50 Combine like terms: 50 + -50 = 0 0 + y = 64.031242374 + -50 y = 64.031242374 + -50 Combine like terms: 64.031242374 + -50 = 14.031242374 y = 14.031242374 Simplifying y = 14.031242374Subproblem 2
y + 50 = -64.031242374 Simplifying y + 50 = -64.031242374 Reorder the terms: 50 + y = -64.031242374 Solving 50 + y = -64.031242374 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + y = -64.031242374 + -50 Combine like terms: 50 + -50 = 0 0 + y = -64.031242374 + -50 y = -64.031242374 + -50 Combine like terms: -64.031242374 + -50 = -114.031242374 y = -114.031242374 Simplifying y = -114.031242374Solution
The solution to the problem is based on the solutions from the subproblems. y = {14.031242374, -114.031242374}Solution
y = {14.031242374, -114.031242374}
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