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Simplifying (-6y2 + -5y) + (7y2 + y + -6) = 0 Reorder the terms: (-5y + -6y2) + (7y2 + y + -6) = 0 Remove parenthesis around (-5y + -6y2) -5y + -6y2 + (7y2 + y + -6) = 0 Reorder the terms: -5y + -6y2 + (-6 + y + 7y2) = 0 Remove parenthesis around (-6 + y + 7y2) -5y + -6y2 + -6 + y + 7y2 = 0 Reorder the terms: -6 + -5y + y + -6y2 + 7y2 = 0 Combine like terms: -5y + y = -4y -6 + -4y + -6y2 + 7y2 = 0 Combine like terms: -6y2 + 7y2 = 1y2 -6 + -4y + 1y2 = 0 Solving -6 + -4y + 1y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + -4y + 6 + y2 = 0 + 6 Reorder the terms: -6 + 6 + -4y + y2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -4y + y2 = 0 + 6 -4y + y2 = 0 + 6 Combine like terms: 0 + 6 = 6 -4y + y2 = 6 The y term is -4y. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4y + 4 + y2 = 6 + 4 Reorder the terms: 4 + -4y + y2 = 6 + 4 Combine like terms: 6 + 4 = 10 4 + -4y + y2 = 10 Factor a perfect square on the left side: (y + -2)(y + -2) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (y + -2) equal to 3.16227766 and -3.16227766.Subproblem 1
y + -2 = 3.16227766 Simplifying y + -2 = 3.16227766 Reorder the terms: -2 + y = 3.16227766 Solving -2 + y = 3.16227766 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = 3.16227766 + 2 Combine like terms: -2 + 2 = 0 0 + y = 3.16227766 + 2 y = 3.16227766 + 2 Combine like terms: 3.16227766 + 2 = 5.16227766 y = 5.16227766 Simplifying y = 5.16227766Subproblem 2
y + -2 = -3.16227766 Simplifying y + -2 = -3.16227766 Reorder the terms: -2 + y = -3.16227766 Solving -2 + y = -3.16227766 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = -3.16227766 + 2 Combine like terms: -2 + 2 = 0 0 + y = -3.16227766 + 2 y = -3.16227766 + 2 Combine like terms: -3.16227766 + 2 = -1.16227766 y = -1.16227766 Simplifying y = -1.16227766Solution
The solution to the problem is based on the solutions from the subproblems. y = {5.16227766, -1.16227766}
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