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Simplifying (5y2 + -1y + -7) + (6y2 + -2y + 4) = 0 Reorder the terms: (-7 + -1y + 5y2) + (6y2 + -2y + 4) = 0 Remove parenthesis around (-7 + -1y + 5y2) -7 + -1y + 5y2 + (6y2 + -2y + 4) = 0 Reorder the terms: -7 + -1y + 5y2 + (4 + -2y + 6y2) = 0 Remove parenthesis around (4 + -2y + 6y2) -7 + -1y + 5y2 + 4 + -2y + 6y2 = 0 Reorder the terms: -7 + 4 + -1y + -2y + 5y2 + 6y2 = 0 Combine like terms: -7 + 4 = -3 -3 + -1y + -2y + 5y2 + 6y2 = 0 Combine like terms: -1y + -2y = -3y -3 + -3y + 5y2 + 6y2 = 0 Combine like terms: 5y2 + 6y2 = 11y2 -3 + -3y + 11y2 = 0 Solving -3 + -3y + 11y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.2727272727 + -0.2727272727y + y2 = 0 Move the constant term to the right: Add '0.2727272727' to each side of the equation. -0.2727272727 + -0.2727272727y + 0.2727272727 + y2 = 0 + 0.2727272727 Reorder the terms: -0.2727272727 + 0.2727272727 + -0.2727272727y + y2 = 0 + 0.2727272727 Combine like terms: -0.2727272727 + 0.2727272727 = 0.0000000000 0.0000000000 + -0.2727272727y + y2 = 0 + 0.2727272727 -0.2727272727y + y2 = 0 + 0.2727272727 Combine like terms: 0 + 0.2727272727 = 0.2727272727 -0.2727272727y + y2 = 0.2727272727 The y term is -0.2727272727y. Take half its coefficient (-0.1363636364). Square it (0.01859504133) and add it to both sides. Add '0.01859504133' to each side of the equation. -0.2727272727y + 0.01859504133 + y2 = 0.2727272727 + 0.01859504133 Reorder the terms: 0.01859504133 + -0.2727272727y + y2 = 0.2727272727 + 0.01859504133 Combine like terms: 0.2727272727 + 0.01859504133 = 0.29132231403 0.01859504133 + -0.2727272727y + y2 = 0.29132231403 Factor a perfect square on the left side: (y + -0.1363636364)(y + -0.1363636364) = 0.29132231403 Calculate the square root of the right side: 0.539742822 Break this problem into two subproblems by setting (y + -0.1363636364) equal to 0.539742822 and -0.539742822.Subproblem 1
y + -0.1363636364 = 0.539742822 Simplifying y + -0.1363636364 = 0.539742822 Reorder the terms: -0.1363636364 + y = 0.539742822 Solving -0.1363636364 + y = 0.539742822 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.1363636364' to each side of the equation. -0.1363636364 + 0.1363636364 + y = 0.539742822 + 0.1363636364 Combine like terms: -0.1363636364 + 0.1363636364 = 0.0000000000 0.0000000000 + y = 0.539742822 + 0.1363636364 y = 0.539742822 + 0.1363636364 Combine like terms: 0.539742822 + 0.1363636364 = 0.6761064584 y = 0.6761064584 Simplifying y = 0.6761064584Subproblem 2
y + -0.1363636364 = -0.539742822 Simplifying y + -0.1363636364 = -0.539742822 Reorder the terms: -0.1363636364 + y = -0.539742822 Solving -0.1363636364 + y = -0.539742822 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.1363636364' to each side of the equation. -0.1363636364 + 0.1363636364 + y = -0.539742822 + 0.1363636364 Combine like terms: -0.1363636364 + 0.1363636364 = 0.0000000000 0.0000000000 + y = -0.539742822 + 0.1363636364 y = -0.539742822 + 0.1363636364 Combine like terms: -0.539742822 + 0.1363636364 = -0.4033791856 y = -0.4033791856 Simplifying y = -0.4033791856Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.6761064584, -0.4033791856}
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