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Simplifying (-3y2 + -9y) + (9y2 + y + -3) = 0 Reorder the terms: (-9y + -3y2) + (9y2 + y + -3) = 0 Remove parenthesis around (-9y + -3y2) -9y + -3y2 + (9y2 + y + -3) = 0 Reorder the terms: -9y + -3y2 + (-3 + y + 9y2) = 0 Remove parenthesis around (-3 + y + 9y2) -9y + -3y2 + -3 + y + 9y2 = 0 Reorder the terms: -3 + -9y + y + -3y2 + 9y2 = 0 Combine like terms: -9y + y = -8y -3 + -8y + -3y2 + 9y2 = 0 Combine like terms: -3y2 + 9y2 = 6y2 -3 + -8y + 6y2 = 0 Solving -3 + -8y + 6y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.5 + -1.333333333y + y2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -1.333333333y + 0.5 + y2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -1.333333333y + y2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -1.333333333y + y2 = 0 + 0.5 -1.333333333y + y2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -1.333333333y + y2 = 0.5 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 = 0.5 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333y + y2 = 0.5 + 0.4444444442 Combine like terms: 0.5 + 0.4444444442 = 0.9444444442 0.4444444442 + -1.333333333y + y2 = 0.9444444442 Factor a perfect square on the left side: (y + -0.6666666665)(y + -0.6666666665) = 0.9444444442 Calculate the square root of the right side: 0.971825316 Break this problem into two subproblems by setting (y + -0.6666666665) equal to 0.971825316 and -0.971825316.Subproblem 1
y + -0.6666666665 = 0.971825316 Simplifying y + -0.6666666665 = 0.971825316 Reorder the terms: -0.6666666665 + y = 0.971825316 Solving -0.6666666665 + y = 0.971825316 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 = 0.971825316 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + y = 0.971825316 + 0.6666666665 y = 0.971825316 + 0.6666666665 Combine like terms: 0.971825316 + 0.6666666665 = 1.6384919825 y = 1.6384919825 Simplifying y = 1.6384919825Subproblem 2
y + -0.6666666665 = -0.971825316 Simplifying y + -0.6666666665 = -0.971825316 Reorder the terms: -0.6666666665 + y = -0.971825316 Solving -0.6666666665 + y = -0.971825316 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 = -0.971825316 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + y = -0.971825316 + 0.6666666665 y = -0.971825316 + 0.6666666665 Combine like terms: -0.971825316 + 0.6666666665 = -0.3051586495 y = -0.3051586495 Simplifying y = -0.3051586495Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.6384919825, -0.3051586495}
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