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Simplifying (-6y2 + -8) + (7y2 + 2y + -5) = 0 Reorder the terms: (-8 + -6y2) + (7y2 + 2y + -5) = 0 Remove parenthesis around (-8 + -6y2) -8 + -6y2 + (7y2 + 2y + -5) = 0 Reorder the terms: -8 + -6y2 + (-5 + 2y + 7y2) = 0 Remove parenthesis around (-5 + 2y + 7y2) -8 + -6y2 + -5 + 2y + 7y2 = 0 Reorder the terms: -8 + -5 + 2y + -6y2 + 7y2 = 0 Combine like terms: -8 + -5 = -13 -13 + 2y + -6y2 + 7y2 = 0 Combine like terms: -6y2 + 7y2 = 1y2 -13 + 2y + 1y2 = 0 Solving -13 + 2y + 1y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + 2y + 13 + y2 = 0 + 13 Reorder the terms: -13 + 13 + 2y + y2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 2y + y2 = 0 + 13 2y + y2 = 0 + 13 Combine like terms: 0 + 13 = 13 2y + y2 = 13 The y term is 2y. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2y + 1 + y2 = 13 + 1 Reorder the terms: 1 + 2y + y2 = 13 + 1 Combine like terms: 13 + 1 = 14 1 + 2y + y2 = 14 Factor a perfect square on the left side: (y + 1)(y + 1) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (y + 1) equal to 3.741657387 and -3.741657387.Subproblem 1
y + 1 = 3.741657387 Simplifying y + 1 = 3.741657387 Reorder the terms: 1 + y = 3.741657387 Solving 1 + y = 3.741657387 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = 3.741657387 + -1 Combine like terms: 1 + -1 = 0 0 + y = 3.741657387 + -1 y = 3.741657387 + -1 Combine like terms: 3.741657387 + -1 = 2.741657387 y = 2.741657387 Simplifying y = 2.741657387Subproblem 2
y + 1 = -3.741657387 Simplifying y + 1 = -3.741657387 Reorder the terms: 1 + y = -3.741657387 Solving 1 + y = -3.741657387 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = -3.741657387 + -1 Combine like terms: 1 + -1 = 0 0 + y = -3.741657387 + -1 y = -3.741657387 + -1 Combine like terms: -3.741657387 + -1 = -4.741657387 y = -4.741657387 Simplifying y = -4.741657387Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.741657387, -4.741657387}
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