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Simplifying -2y2 + -10y + 64 = 0 Reorder the terms: 64 + -10y + -2y2 = 0 Solving 64 + -10y + -2y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(32 + -5y + -1y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(32 + -5y + -1y2)' equal to zero and attempt to solve: Simplifying 32 + -5y + -1y2 = 0 Solving 32 + -5y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -32 + 5y + y2 = 0 Move the constant term to the right: Add '32' to each side of the equation. -32 + 5y + 32 + y2 = 0 + 32 Reorder the terms: -32 + 32 + 5y + y2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + 5y + y2 = 0 + 32 5y + y2 = 0 + 32 Combine like terms: 0 + 32 = 32 5y + y2 = 32 The y term is 5y. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5y + 6.25 + y2 = 32 + 6.25 Reorder the terms: 6.25 + 5y + y2 = 32 + 6.25 Combine like terms: 32 + 6.25 = 38.25 6.25 + 5y + y2 = 38.25 Factor a perfect square on the left side: (y + 2.5)(y + 2.5) = 38.25 Calculate the square root of the right side: 6.184658438 Break this problem into two subproblems by setting (y + 2.5) equal to 6.184658438 and -6.184658438.Subproblem 1
y + 2.5 = 6.184658438 Simplifying y + 2.5 = 6.184658438 Reorder the terms: 2.5 + y = 6.184658438 Solving 2.5 + y = 6.184658438 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + y = 6.184658438 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + y = 6.184658438 + -2.5 y = 6.184658438 + -2.5 Combine like terms: 6.184658438 + -2.5 = 3.684658438 y = 3.684658438 Simplifying y = 3.684658438Subproblem 2
y + 2.5 = -6.184658438 Simplifying y + 2.5 = -6.184658438 Reorder the terms: 2.5 + y = -6.184658438 Solving 2.5 + y = -6.184658438 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + y = -6.184658438 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + y = -6.184658438 + -2.5 y = -6.184658438 + -2.5 Combine like terms: -6.184658438 + -2.5 = -8.684658438 y = -8.684658438 Simplifying y = -8.684658438Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.684658438, -8.684658438}Solution
y = {3.684658438, -8.684658438}
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