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Simplifying 2y2 + -4y + -8 = -1y2 + 4 Reorder the terms: -8 + -4y + 2y2 = -1y2 + 4 Reorder the terms: -8 + -4y + 2y2 = 4 + -1y2 Solving -8 + -4y + 2y2 = 4 + -1y2 Solving for variable 'y'. Reorder the terms: -8 + -4 + -4y + 2y2 + y2 = 4 + -1y2 + -4 + y2 Combine like terms: -8 + -4 = -12 -12 + -4y + 2y2 + y2 = 4 + -1y2 + -4 + y2 Combine like terms: 2y2 + y2 = 3y2 -12 + -4y + 3y2 = 4 + -1y2 + -4 + y2 Reorder the terms: -12 + -4y + 3y2 = 4 + -4 + -1y2 + y2 Combine like terms: 4 + -4 = 0 -12 + -4y + 3y2 = 0 + -1y2 + y2 -12 + -4y + 3y2 = -1y2 + y2 Combine like terms: -1y2 + y2 = 0 -12 + -4y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -4 + -1.333333333y + y2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -1.333333333y + 4 + y2 = 0 + 4 Reorder the terms: -4 + 4 + -1.333333333y + y2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1.333333333y + y2 = 0 + 4 -1.333333333y + y2 = 0 + 4 Combine like terms: 0 + 4 = 4 -1.333333333y + y2 = 4 The y term is -1.333333333y. Take half its coefficient (-0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. -1.333333333y + 0.4444444442 + y2 = 4 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333y + y2 = 4 + 0.4444444442 Combine like terms: 4 + 0.4444444442 = 4.4444444442 0.4444444442 + -1.333333333y + y2 = 4.4444444442 Factor a perfect square on the left side: (y + -0.6666666665)(y + -0.6666666665) = 4.4444444442 Calculate the square root of the right side: 2.108185107 Break this problem into two subproblems by setting (y + -0.6666666665) equal to 2.108185107 and -2.108185107.Subproblem 1
y + -0.6666666665 = 2.108185107 Simplifying y + -0.6666666665 = 2.108185107 Reorder the terms: -0.6666666665 + y = 2.108185107 Solving -0.6666666665 + y = 2.108185107 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + y = 2.108185107 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + y = 2.108185107 + 0.6666666665 y = 2.108185107 + 0.6666666665 Combine like terms: 2.108185107 + 0.6666666665 = 2.7748517735 y = 2.7748517735 Simplifying y = 2.7748517735Subproblem 2
y + -0.6666666665 = -2.108185107 Simplifying y + -0.6666666665 = -2.108185107 Reorder the terms: -0.6666666665 + y = -2.108185107 Solving -0.6666666665 + y = -2.108185107 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + y = -2.108185107 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + y = -2.108185107 + 0.6666666665 y = -2.108185107 + 0.6666666665 Combine like terms: -2.108185107 + 0.6666666665 = -1.4415184405 y = -1.4415184405 Simplifying y = -1.4415184405Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.7748517735, -1.4415184405}
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