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Simplifying (6y2 + 8y) + -1(-3y2 + -4y + 8) = 0 Reorder the terms: (8y + 6y2) + -1(-3y2 + -4y + 8) = 0 Remove parenthesis around (8y + 6y2) 8y + 6y2 + -1(-3y2 + -4y + 8) = 0 Reorder the terms: 8y + 6y2 + -1(8 + -4y + -3y2) = 0 8y + 6y2 + (8 * -1 + -4y * -1 + -3y2 * -1) = 0 8y + 6y2 + (-8 + 4y + 3y2) = 0 Reorder the terms: -8 + 8y + 4y + 6y2 + 3y2 = 0 Combine like terms: 8y + 4y = 12y -8 + 12y + 6y2 + 3y2 = 0 Combine like terms: 6y2 + 3y2 = 9y2 -8 + 12y + 9y2 = 0 Solving -8 + 12y + 9y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.8888888889 + 1.333333333y + y2 = 0 Move the constant term to the right: Add '0.8888888889' to each side of the equation. -0.8888888889 + 1.333333333y + 0.8888888889 + y2 = 0 + 0.8888888889 Reorder the terms: -0.8888888889 + 0.8888888889 + 1.333333333y + y2 = 0 + 0.8888888889 Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000 0.0000000000 + 1.333333333y + y2 = 0 + 0.8888888889 1.333333333y + y2 = 0 + 0.8888888889 Combine like terms: 0 + 0.8888888889 = 0.8888888889 1.333333333y + y2 = 0.8888888889 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 = 0.8888888889 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333y + y2 = 0.8888888889 + 0.4444444442 Combine like terms: 0.8888888889 + 0.4444444442 = 1.3333333331 0.4444444442 + 1.333333333y + y2 = 1.3333333331 Factor a perfect square on the left side: (y + 0.6666666665)(y + 0.6666666665) = 1.3333333331 Calculate the square root of the right side: 1.154700538 Break this problem into two subproblems by setting (y + 0.6666666665) equal to 1.154700538 and -1.154700538.Subproblem 1
y + 0.6666666665 = 1.154700538 Simplifying y + 0.6666666665 = 1.154700538 Reorder the terms: 0.6666666665 + y = 1.154700538 Solving 0.6666666665 + y = 1.154700538 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 = 1.154700538 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + y = 1.154700538 + -0.6666666665 y = 1.154700538 + -0.6666666665 Combine like terms: 1.154700538 + -0.6666666665 = 0.4880338715 y = 0.4880338715 Simplifying y = 0.4880338715Subproblem 2
y + 0.6666666665 = -1.154700538 Simplifying y + 0.6666666665 = -1.154700538 Reorder the terms: 0.6666666665 + y = -1.154700538 Solving 0.6666666665 + y = -1.154700538 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 = -1.154700538 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + y = -1.154700538 + -0.6666666665 y = -1.154700538 + -0.6666666665 Combine like terms: -1.154700538 + -0.6666666665 = -1.8213672045 y = -1.8213672045 Simplifying y = -1.8213672045Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.4880338715, -1.8213672045}
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