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Simplifying -25y2 + -60y + 60 = 0 Reorder the terms: 60 + -60y + -25y2 = 0 Solving 60 + -60y + -25y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '5'. 5(12 + -12y + -5y2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(12 + -12y + -5y2)' equal to zero and attempt to solve: Simplifying 12 + -12y + -5y2 = 0 Solving 12 + -12y + -5y2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -2.4 + 2.4y + y2 = 0 Move the constant term to the right: Add '2.4' to each side of the equation. -2.4 + 2.4y + 2.4 + y2 = 0 + 2.4 Reorder the terms: -2.4 + 2.4 + 2.4y + y2 = 0 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + 2.4y + y2 = 0 + 2.4 2.4y + y2 = 0 + 2.4 Combine like terms: 0 + 2.4 = 2.4 2.4y + y2 = 2.4 The y term is 2.4y. Take half its coefficient (1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. 2.4y + 1.44 + y2 = 2.4 + 1.44 Reorder the terms: 1.44 + 2.4y + y2 = 2.4 + 1.44 Combine like terms: 2.4 + 1.44 = 3.84 1.44 + 2.4y + y2 = 3.84 Factor a perfect square on the left side: (y + 1.2)(y + 1.2) = 3.84 Calculate the square root of the right side: 1.959591794 Break this problem into two subproblems by setting (y + 1.2) equal to 1.959591794 and -1.959591794.Subproblem 1
y + 1.2 = 1.959591794 Simplifying y + 1.2 = 1.959591794 Reorder the terms: 1.2 + y = 1.959591794 Solving 1.2 + y = 1.959591794 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + y = 1.959591794 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + y = 1.959591794 + -1.2 y = 1.959591794 + -1.2 Combine like terms: 1.959591794 + -1.2 = 0.759591794 y = 0.759591794 Simplifying y = 0.759591794Subproblem 2
y + 1.2 = -1.959591794 Simplifying y + 1.2 = -1.959591794 Reorder the terms: 1.2 + y = -1.959591794 Solving 1.2 + y = -1.959591794 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + y = -1.959591794 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + y = -1.959591794 + -1.2 y = -1.959591794 + -1.2 Combine like terms: -1.959591794 + -1.2 = -3.159591794 y = -3.159591794 Simplifying y = -3.159591794Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.759591794, -3.159591794}Solution
y = {0.759591794, -3.159591794}
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