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Simplifying -12 = y2 + 20y Reorder the terms: -12 = 20y + y2 Solving -12 = 20y + y2 Solving for variable 'y'. Reorder the terms: -12 + -20y + -1y2 = 20y + -20y + y2 + -1y2 Combine like terms: 20y + -20y = 0 -12 + -20y + -1y2 = 0 + y2 + -1y2 -12 + -20y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 -12 + -20y + -1y2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(12 + 20y + y2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(12 + 20y + y2)' equal to zero and attempt to solve: Simplifying 12 + 20y + y2 = 0 Solving 12 + 20y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + 20y + -12 + y2 = 0 + -12 Reorder the terms: 12 + -12 + 20y + y2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 20y + y2 = 0 + -12 20y + y2 = 0 + -12 Combine like terms: 0 + -12 = -12 20y + y2 = -12 The y term is 20y. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20y + 100 + y2 = -12 + 100 Reorder the terms: 100 + 20y + y2 = -12 + 100 Combine like terms: -12 + 100 = 88 100 + 20y + y2 = 88 Factor a perfect square on the left side: (y + 10)(y + 10) = 88 Calculate the square root of the right side: 9.38083152 Break this problem into two subproblems by setting (y + 10) equal to 9.38083152 and -9.38083152.Subproblem 1
y + 10 = 9.38083152 Simplifying y + 10 = 9.38083152 Reorder the terms: 10 + y = 9.38083152 Solving 10 + y = 9.38083152 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + y = 9.38083152 + -10 Combine like terms: 10 + -10 = 0 0 + y = 9.38083152 + -10 y = 9.38083152 + -10 Combine like terms: 9.38083152 + -10 = -0.61916848 y = -0.61916848 Simplifying y = -0.61916848Subproblem 2
y + 10 = -9.38083152 Simplifying y + 10 = -9.38083152 Reorder the terms: 10 + y = -9.38083152 Solving 10 + y = -9.38083152 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + y = -9.38083152 + -10 Combine like terms: 10 + -10 = 0 0 + y = -9.38083152 + -10 y = -9.38083152 + -10 Combine like terms: -9.38083152 + -10 = -19.38083152 y = -19.38083152 Simplifying y = -19.38083152Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.61916848, -19.38083152}Solution
y = {-0.61916848, -19.38083152}
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