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Simplifying (5y2 + 9) + (8y + 1) + -1(7y2 + -2y + -5) = 0 Reorder the terms: (9 + 5y2) + (8y + 1) + -1(7y2 + -2y + -5) = 0 Remove parenthesis around (9 + 5y2) 9 + 5y2 + (8y + 1) + -1(7y2 + -2y + -5) = 0 Reorder the terms: 9 + 5y2 + (1 + 8y) + -1(7y2 + -2y + -5) = 0 Remove parenthesis around (1 + 8y) 9 + 5y2 + 1 + 8y + -1(7y2 + -2y + -5) = 0 Reorder the terms: 9 + 5y2 + 1 + 8y + -1(-5 + -2y + 7y2) = 0 9 + 5y2 + 1 + 8y + (-5 * -1 + -2y * -1 + 7y2 * -1) = 0 9 + 5y2 + 1 + 8y + (5 + 2y + -7y2) = 0 Reorder the terms: 9 + 1 + 5 + 8y + 2y + 5y2 + -7y2 = 0 Combine like terms: 9 + 1 = 10 10 + 5 + 8y + 2y + 5y2 + -7y2 = 0 Combine like terms: 10 + 5 = 15 15 + 8y + 2y + 5y2 + -7y2 = 0 Combine like terms: 8y + 2y = 10y 15 + 10y + 5y2 + -7y2 = 0 Combine like terms: 5y2 + -7y2 = -2y2 15 + 10y + -2y2 = 0 Solving 15 + 10y + -2y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -7.5 + -5y + y2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + -5y + 7.5 + y2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + -5y + y2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + -5y + y2 = 0 + 7.5 -5y + y2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 -5y + y2 = 7.5 The y term is -5y. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5y + 6.25 + y2 = 7.5 + 6.25 Reorder the terms: 6.25 + -5y + y2 = 7.5 + 6.25 Combine like terms: 7.5 + 6.25 = 13.75 6.25 + -5y + y2 = 13.75 Factor a perfect square on the left side: (y + -2.5)(y + -2.5) = 13.75 Calculate the square root of the right side: 3.708099244 Break this problem into two subproblems by setting (y + -2.5) equal to 3.708099244 and -3.708099244.Subproblem 1
y + -2.5 = 3.708099244 Simplifying y + -2.5 = 3.708099244 Reorder the terms: -2.5 + y = 3.708099244 Solving -2.5 + y = 3.708099244 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + y = 3.708099244 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + y = 3.708099244 + 2.5 y = 3.708099244 + 2.5 Combine like terms: 3.708099244 + 2.5 = 6.208099244 y = 6.208099244 Simplifying y = 6.208099244Subproblem 2
y + -2.5 = -3.708099244 Simplifying y + -2.5 = -3.708099244 Reorder the terms: -2.5 + y = -3.708099244 Solving -2.5 + y = -3.708099244 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + y = -3.708099244 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + y = -3.708099244 + 2.5 y = -3.708099244 + 2.5 Combine like terms: -3.708099244 + 2.5 = -1.208099244 y = -1.208099244 Simplifying y = -1.208099244Solution
The solution to the problem is based on the solutions from the subproblems. y = {6.208099244, -1.208099244}
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