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Simplifying -3y2 = 6y + -10 Reorder the terms: -3y2 = -10 + 6y Solving -3y2 = -10 + 6y Solving for variable 'y'. Reorder the terms: 10 + -6y + -3y2 = -10 + 6y + 10 + -6y Reorder the terms: 10 + -6y + -3y2 = -10 + 10 + 6y + -6y Combine like terms: -10 + 10 = 0 10 + -6y + -3y2 = 0 + 6y + -6y 10 + -6y + -3y2 = 6y + -6y Combine like terms: 6y + -6y = 0 10 + -6y + -3y2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -3.333333333 + 2y + y2 = 0 Move the constant term to the right: Add '3.333333333' to each side of the equation. -3.333333333 + 2y + 3.333333333 + y2 = 0 + 3.333333333 Reorder the terms: -3.333333333 + 3.333333333 + 2y + y2 = 0 + 3.333333333 Combine like terms: -3.333333333 + 3.333333333 = 0.000000000 0.000000000 + 2y + y2 = 0 + 3.333333333 2y + y2 = 0 + 3.333333333 Combine like terms: 0 + 3.333333333 = 3.333333333 2y + y2 = 3.333333333 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 = 3.333333333 + 1 Reorder the terms: 1 + 2y + y2 = 3.333333333 + 1 Combine like terms: 3.333333333 + 1 = 4.333333333 1 + 2y + y2 = 4.333333333 Factor a perfect square on the left side: (y + 1)(y + 1) = 4.333333333 Calculate the square root of the right side: 2.081665999 Break this problem into two subproblems by setting (y + 1) equal to 2.081665999 and -2.081665999.Subproblem 1
y + 1 = 2.081665999 Simplifying y + 1 = 2.081665999 Reorder the terms: 1 + y = 2.081665999 Solving 1 + y = 2.081665999 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 = 2.081665999 + -1 Combine like terms: 1 + -1 = 0 0 + y = 2.081665999 + -1 y = 2.081665999 + -1 Combine like terms: 2.081665999 + -1 = 1.081665999 y = 1.081665999 Simplifying y = 1.081665999Subproblem 2
y + 1 = -2.081665999 Simplifying y + 1 = -2.081665999 Reorder the terms: 1 + y = -2.081665999 Solving 1 + y = -2.081665999 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 = -2.081665999 + -1 Combine like terms: 1 + -1 = 0 0 + y = -2.081665999 + -1 y = -2.081665999 + -1 Combine like terms: -2.081665999 + -1 = -3.081665999 y = -3.081665999 Simplifying y = -3.081665999Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.081665999, -3.081665999}
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