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Simplifying 8y2 + 16y + -160 = 0 Reorder the terms: -160 + 16y + 8y2 = 0 Solving -160 + 16y + 8y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '8'. 8(-20 + 2y + y2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-20 + 2y + y2)' equal to zero and attempt to solve: Simplifying -20 + 2y + y2 = 0 Solving -20 + 2y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + 2y + 20 + y2 = 0 + 20 Reorder the terms: -20 + 20 + 2y + y2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 2y + y2 = 0 + 20 2y + y2 = 0 + 20 Combine like terms: 0 + 20 = 20 2y + y2 = 20 The y term is 2y. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2y + 1 + y2 = 20 + 1 Reorder the terms: 1 + 2y + y2 = 20 + 1 Combine like terms: 20 + 1 = 21 1 + 2y + y2 = 21 Factor a perfect square on the left side: (y + 1)(y + 1) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (y + 1) equal to 4.582575695 and -4.582575695.Subproblem 1
y + 1 = 4.582575695 Simplifying y + 1 = 4.582575695 Reorder the terms: 1 + y = 4.582575695 Solving 1 + y = 4.582575695 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = 4.582575695 + -1 Combine like terms: 1 + -1 = 0 0 + y = 4.582575695 + -1 y = 4.582575695 + -1 Combine like terms: 4.582575695 + -1 = 3.582575695 y = 3.582575695 Simplifying y = 3.582575695Subproblem 2
y + 1 = -4.582575695 Simplifying y + 1 = -4.582575695 Reorder the terms: 1 + y = -4.582575695 Solving 1 + y = -4.582575695 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = -4.582575695 + -1 Combine like terms: 1 + -1 = 0 0 + y = -4.582575695 + -1 y = -4.582575695 + -1 Combine like terms: -4.582575695 + -1 = -5.582575695 y = -5.582575695 Simplifying y = -5.582575695Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.582575695, -5.582575695}Solution
y = {3.582575695, -5.582575695}
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