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Simplifying 2y2 = 39y + -17 Reorder the terms: 2y2 = -17 + 39y Solving 2y2 = -17 + 39y Solving for variable 'y'. Reorder the terms: 17 + -39y + 2y2 = -17 + 39y + 17 + -39y Reorder the terms: 17 + -39y + 2y2 = -17 + 17 + 39y + -39y Combine like terms: -17 + 17 = 0 17 + -39y + 2y2 = 0 + 39y + -39y 17 + -39y + 2y2 = 39y + -39y Combine like terms: 39y + -39y = 0 17 + -39y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 8.5 + -19.5y + y2 = 0 Move the constant term to the right: Add '-8.5' to each side of the equation. 8.5 + -19.5y + -8.5 + y2 = 0 + -8.5 Reorder the terms: 8.5 + -8.5 + -19.5y + y2 = 0 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + -19.5y + y2 = 0 + -8.5 -19.5y + y2 = 0 + -8.5 Combine like terms: 0 + -8.5 = -8.5 -19.5y + y2 = -8.5 The y term is -19.5y. Take half its coefficient (-9.75). Square it (95.0625) and add it to both sides. Add '95.0625' to each side of the equation. -19.5y + 95.0625 + y2 = -8.5 + 95.0625 Reorder the terms: 95.0625 + -19.5y + y2 = -8.5 + 95.0625 Combine like terms: -8.5 + 95.0625 = 86.5625 95.0625 + -19.5y + y2 = 86.5625 Factor a perfect square on the left side: (y + -9.75)(y + -9.75) = 86.5625 Calculate the square root of the right side: 9.303897033 Break this problem into two subproblems by setting (y + -9.75) equal to 9.303897033 and -9.303897033.Subproblem 1
y + -9.75 = 9.303897033 Simplifying y + -9.75 = 9.303897033 Reorder the terms: -9.75 + y = 9.303897033 Solving -9.75 + y = 9.303897033 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '9.75' to each side of the equation. -9.75 + 9.75 + y = 9.303897033 + 9.75 Combine like terms: -9.75 + 9.75 = 0.00 0.00 + y = 9.303897033 + 9.75 y = 9.303897033 + 9.75 Combine like terms: 9.303897033 + 9.75 = 19.053897033 y = 19.053897033 Simplifying y = 19.053897033Subproblem 2
y + -9.75 = -9.303897033 Simplifying y + -9.75 = -9.303897033 Reorder the terms: -9.75 + y = -9.303897033 Solving -9.75 + y = -9.303897033 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '9.75' to each side of the equation. -9.75 + 9.75 + y = -9.303897033 + 9.75 Combine like terms: -9.75 + 9.75 = 0.00 0.00 + y = -9.303897033 + 9.75 y = -9.303897033 + 9.75 Combine like terms: -9.303897033 + 9.75 = 0.446102967 y = 0.446102967 Simplifying y = 0.446102967Solution
The solution to the problem is based on the solutions from the subproblems. y = {19.053897033, 0.446102967}
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