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Simplifying (9y2 + 5y + 2) + -1(2y2 + -5y + 9) = 0 Reorder the terms: (2 + 5y + 9y2) + -1(2y2 + -5y + 9) = 0 Remove parenthesis around (2 + 5y + 9y2) 2 + 5y + 9y2 + -1(2y2 + -5y + 9) = 0 Reorder the terms: 2 + 5y + 9y2 + -1(9 + -5y + 2y2) = 0 2 + 5y + 9y2 + (9 * -1 + -5y * -1 + 2y2 * -1) = 0 2 + 5y + 9y2 + (-9 + 5y + -2y2) = 0 Reorder the terms: 2 + -9 + 5y + 5y + 9y2 + -2y2 = 0 Combine like terms: 2 + -9 = -7 -7 + 5y + 5y + 9y2 + -2y2 = 0 Combine like terms: 5y + 5y = 10y -7 + 10y + 9y2 + -2y2 = 0 Combine like terms: 9y2 + -2y2 = 7y2 -7 + 10y + 7y2 = 0 Solving -7 + 10y + 7y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1 + 1.428571429y + y2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 1.428571429y + 1 + y2 = 0 + 1 Reorder the terms: -1 + 1 + 1.428571429y + y2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 1.428571429y + y2 = 0 + 1 1.428571429y + y2 = 0 + 1 Combine like terms: 0 + 1 = 1 1.428571429y + y2 = 1 The y term is 1.428571429y. Take half its coefficient (0.7142857145). Square it (0.5102040819) and add it to both sides. Add '0.5102040819' to each side of the equation. 1.428571429y + 0.5102040819 + y2 = 1 + 0.5102040819 Reorder the terms: 0.5102040819 + 1.428571429y + y2 = 1 + 0.5102040819 Combine like terms: 1 + 0.5102040819 = 1.5102040819 0.5102040819 + 1.428571429y + y2 = 1.5102040819 Factor a perfect square on the left side: (y + 0.7142857145)(y + 0.7142857145) = 1.5102040819 Calculate the square root of the right side: 1.22890361 Break this problem into two subproblems by setting (y + 0.7142857145) equal to 1.22890361 and -1.22890361.Subproblem 1
y + 0.7142857145 = 1.22890361 Simplifying y + 0.7142857145 = 1.22890361 Reorder the terms: 0.7142857145 + y = 1.22890361 Solving 0.7142857145 + y = 1.22890361 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.7142857145' to each side of the equation. 0.7142857145 + -0.7142857145 + y = 1.22890361 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + y = 1.22890361 + -0.7142857145 y = 1.22890361 + -0.7142857145 Combine like terms: 1.22890361 + -0.7142857145 = 0.5146178955 y = 0.5146178955 Simplifying y = 0.5146178955Subproblem 2
y + 0.7142857145 = -1.22890361 Simplifying y + 0.7142857145 = -1.22890361 Reorder the terms: 0.7142857145 + y = -1.22890361 Solving 0.7142857145 + y = -1.22890361 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.7142857145' to each side of the equation. 0.7142857145 + -0.7142857145 + y = -1.22890361 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + y = -1.22890361 + -0.7142857145 y = -1.22890361 + -0.7142857145 Combine like terms: -1.22890361 + -0.7142857145 = -1.9431893245 y = -1.9431893245 Simplifying y = -1.9431893245Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.5146178955, -1.9431893245}
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