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Simplifying 80.18 = y2 + 15y Reorder the terms: 80.18 = 15y + y2 Solving 80.18 = 15y + y2 Solving for variable 'y'. Reorder the terms: 80.18 + -15y + -1y2 = 15y + -15y + y2 + -1y2 Combine like terms: 15y + -15y = 0 80.18 + -15y + -1y2 = 0 + y2 + -1y2 80.18 + -15y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 80.18 + -15y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -80.18 + 15y + y2 = 0 Move the constant term to the right: Add '80.18' to each side of the equation. -80.18 + 15y + 80.18 + y2 = 0 + 80.18 Reorder the terms: -80.18 + 80.18 + 15y + y2 = 0 + 80.18 Combine like terms: -80.18 + 80.18 = 0.00 0.00 + 15y + y2 = 0 + 80.18 15y + y2 = 0 + 80.18 Combine like terms: 0 + 80.18 = 80.18 15y + y2 = 80.18 The y term is 15y. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15y + 56.25 + y2 = 80.18 + 56.25 Reorder the terms: 56.25 + 15y + y2 = 80.18 + 56.25 Combine like terms: 80.18 + 56.25 = 136.43 56.25 + 15y + y2 = 136.43 Factor a perfect square on the left side: (y + 7.5)(y + 7.5) = 136.43 Calculate the square root of the right side: 11.680325338 Break this problem into two subproblems by setting (y + 7.5) equal to 11.680325338 and -11.680325338.Subproblem 1
y + 7.5 = 11.680325338 Simplifying y + 7.5 = 11.680325338 Reorder the terms: 7.5 + y = 11.680325338 Solving 7.5 + y = 11.680325338 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + y = 11.680325338 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + y = 11.680325338 + -7.5 y = 11.680325338 + -7.5 Combine like terms: 11.680325338 + -7.5 = 4.180325338 y = 4.180325338 Simplifying y = 4.180325338Subproblem 2
y + 7.5 = -11.680325338 Simplifying y + 7.5 = -11.680325338 Reorder the terms: 7.5 + y = -11.680325338 Solving 7.5 + y = -11.680325338 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + y = -11.680325338 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + y = -11.680325338 + -7.5 y = -11.680325338 + -7.5 Combine like terms: -11.680325338 + -7.5 = -19.180325338 y = -19.180325338 Simplifying y = -19.180325338Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.180325338, -19.180325338}
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