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Simplifying -1y2 + -30y + -90 = 0 Reorder the terms: -90 + -30y + -1y2 = 0 Solving -90 + -30y + -1y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '-1'. -1(90 + 30y + y2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(90 + 30y + y2)' equal to zero and attempt to solve: Simplifying 90 + 30y + y2 = 0 Solving 90 + 30y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-90' to each side of the equation. 90 + 30y + -90 + y2 = 0 + -90 Reorder the terms: 90 + -90 + 30y + y2 = 0 + -90 Combine like terms: 90 + -90 = 0 0 + 30y + y2 = 0 + -90 30y + y2 = 0 + -90 Combine like terms: 0 + -90 = -90 30y + y2 = -90 The y term is 30y. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30y + 225 + y2 = -90 + 225 Reorder the terms: 225 + 30y + y2 = -90 + 225 Combine like terms: -90 + 225 = 135 225 + 30y + y2 = 135 Factor a perfect square on the left side: (y + 15)(y + 15) = 135 Calculate the square root of the right side: 11.618950039 Break this problem into two subproblems by setting (y + 15) equal to 11.618950039 and -11.618950039.Subproblem 1
y + 15 = 11.618950039 Simplifying y + 15 = 11.618950039 Reorder the terms: 15 + y = 11.618950039 Solving 15 + y = 11.618950039 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + y = 11.618950039 + -15 Combine like terms: 15 + -15 = 0 0 + y = 11.618950039 + -15 y = 11.618950039 + -15 Combine like terms: 11.618950039 + -15 = -3.381049961 y = -3.381049961 Simplifying y = -3.381049961Subproblem 2
y + 15 = -11.618950039 Simplifying y + 15 = -11.618950039 Reorder the terms: 15 + y = -11.618950039 Solving 15 + y = -11.618950039 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + y = -11.618950039 + -15 Combine like terms: 15 + -15 = 0 0 + y = -11.618950039 + -15 y = -11.618950039 + -15 Combine like terms: -11.618950039 + -15 = -26.618950039 y = -26.618950039 Simplifying y = -26.618950039Solution
The solution to the problem is based on the solutions from the subproblems. y = {-3.381049961, -26.618950039}Solution
y = {-3.381049961, -26.618950039}
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