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Simplifying (-7y2 + -2y + 1) + (-6y2 + 3) = 0 Reorder the terms: (1 + -2y + -7y2) + (-6y2 + 3) = 0 Remove parenthesis around (1 + -2y + -7y2) 1 + -2y + -7y2 + (-6y2 + 3) = 0 Reorder the terms: 1 + -2y + -7y2 + (3 + -6y2) = 0 Remove parenthesis around (3 + -6y2) 1 + -2y + -7y2 + 3 + -6y2 = 0 Reorder the terms: 1 + 3 + -2y + -7y2 + -6y2 = 0 Combine like terms: 1 + 3 = 4 4 + -2y + -7y2 + -6y2 = 0 Combine like terms: -7y2 + -6y2 = -13y2 4 + -2y + -13y2 = 0 Solving 4 + -2y + -13y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by -13 the coefficient of the squared term: Divide each side by '-13'. -0.3076923077 + 0.1538461538y + y2 = 0 Move the constant term to the right: Add '0.3076923077' to each side of the equation. -0.3076923077 + 0.1538461538y + 0.3076923077 + y2 = 0 + 0.3076923077 Reorder the terms: -0.3076923077 + 0.3076923077 + 0.1538461538y + y2 = 0 + 0.3076923077 Combine like terms: -0.3076923077 + 0.3076923077 = 0.0000000000 0.0000000000 + 0.1538461538y + y2 = 0 + 0.3076923077 0.1538461538y + y2 = 0 + 0.3076923077 Combine like terms: 0 + 0.3076923077 = 0.3076923077 0.1538461538y + y2 = 0.3076923077 The y term is 0.1538461538y. Take half its coefficient (0.0769230769). Square it (0.005917159760) and add it to both sides. Add '0.005917159760' to each side of the equation. 0.1538461538y + 0.005917159760 + y2 = 0.3076923077 + 0.005917159760 Reorder the terms: 0.005917159760 + 0.1538461538y + y2 = 0.3076923077 + 0.005917159760 Combine like terms: 0.3076923077 + 0.005917159760 = 0.31360946746 0.005917159760 + 0.1538461538y + y2 = 0.31360946746 Factor a perfect square on the left side: (y + 0.0769230769)(y + 0.0769230769) = 0.31360946746 Calculate the square root of the right side: 0.560008453 Break this problem into two subproblems by setting (y + 0.0769230769) equal to 0.560008453 and -0.560008453.Subproblem 1
y + 0.0769230769 = 0.560008453 Simplifying y + 0.0769230769 = 0.560008453 Reorder the terms: 0.0769230769 + y = 0.560008453 Solving 0.0769230769 + y = 0.560008453 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.0769230769' to each side of the equation. 0.0769230769 + -0.0769230769 + y = 0.560008453 + -0.0769230769 Combine like terms: 0.0769230769 + -0.0769230769 = 0.0000000000 0.0000000000 + y = 0.560008453 + -0.0769230769 y = 0.560008453 + -0.0769230769 Combine like terms: 0.560008453 + -0.0769230769 = 0.4830853761 y = 0.4830853761 Simplifying y = 0.4830853761Subproblem 2
y + 0.0769230769 = -0.560008453 Simplifying y + 0.0769230769 = -0.560008453 Reorder the terms: 0.0769230769 + y = -0.560008453 Solving 0.0769230769 + y = -0.560008453 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.0769230769' to each side of the equation. 0.0769230769 + -0.0769230769 + y = -0.560008453 + -0.0769230769 Combine like terms: 0.0769230769 + -0.0769230769 = 0.0000000000 0.0000000000 + y = -0.560008453 + -0.0769230769 y = -0.560008453 + -0.0769230769 Combine like terms: -0.560008453 + -0.0769230769 = -0.6369315299 y = -0.6369315299 Simplifying y = -0.6369315299Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.4830853761, -0.6369315299}
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