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Simplifying 2y2 + 7y + 15 + -1y2 + 10y + 25 = 0 Reorder the terms: 15 + 25 + 7y + 10y + 2y2 + -1y2 = 0 Combine like terms: 15 + 25 = 40 40 + 7y + 10y + 2y2 + -1y2 = 0 Combine like terms: 7y + 10y = 17y 40 + 17y + 2y2 + -1y2 = 0 Combine like terms: 2y2 + -1y2 = 1y2 40 + 17y + 1y2 = 0 Solving 40 + 17y + 1y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-40' to each side of the equation. 40 + 17y + -40 + y2 = 0 + -40 Reorder the terms: 40 + -40 + 17y + y2 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + 17y + y2 = 0 + -40 17y + y2 = 0 + -40 Combine like terms: 0 + -40 = -40 17y + y2 = -40 The y term is 17y. Take half its coefficient (8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. 17y + 72.25 + y2 = -40 + 72.25 Reorder the terms: 72.25 + 17y + y2 = -40 + 72.25 Combine like terms: -40 + 72.25 = 32.25 72.25 + 17y + y2 = 32.25 Factor a perfect square on the left side: (y + 8.5)(y + 8.5) = 32.25 Calculate the square root of the right side: 5.678908346 Break this problem into two subproblems by setting (y + 8.5) equal to 5.678908346 and -5.678908346.Subproblem 1
y + 8.5 = 5.678908346 Simplifying y + 8.5 = 5.678908346 Reorder the terms: 8.5 + y = 5.678908346 Solving 8.5 + y = 5.678908346 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + y = 5.678908346 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + y = 5.678908346 + -8.5 y = 5.678908346 + -8.5 Combine like terms: 5.678908346 + -8.5 = -2.821091654 y = -2.821091654 Simplifying y = -2.821091654Subproblem 2
y + 8.5 = -5.678908346 Simplifying y + 8.5 = -5.678908346 Reorder the terms: 8.5 + y = -5.678908346 Solving 8.5 + y = -5.678908346 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + y = -5.678908346 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + y = -5.678908346 + -8.5 y = -5.678908346 + -8.5 Combine like terms: -5.678908346 + -8.5 = -14.178908346 y = -14.178908346 Simplifying y = -14.178908346Solution
The solution to the problem is based on the solutions from the subproblems. y = {-2.821091654, -14.178908346}
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