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Simplifying 12y2 + -19y + -35 = 0 Reorder the terms: -35 + -19y + 12y2 = 0 Solving -35 + -19y + 12y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -2.916666667 + -1.583333333y + y2 = 0 Move the constant term to the right: Add '2.916666667' to each side of the equation. -2.916666667 + -1.583333333y + 2.916666667 + y2 = 0 + 2.916666667 Reorder the terms: -2.916666667 + 2.916666667 + -1.583333333y + y2 = 0 + 2.916666667 Combine like terms: -2.916666667 + 2.916666667 = 0.000000000 0.000000000 + -1.583333333y + y2 = 0 + 2.916666667 -1.583333333y + y2 = 0 + 2.916666667 Combine like terms: 0 + 2.916666667 = 2.916666667 -1.583333333y + y2 = 2.916666667 The y term is -1.583333333y. Take half its coefficient (-0.7916666665). Square it (0.6267361108) and add it to both sides. Add '0.6267361108' to each side of the equation. -1.583333333y + 0.6267361108 + y2 = 2.916666667 + 0.6267361108 Reorder the terms: 0.6267361108 + -1.583333333y + y2 = 2.916666667 + 0.6267361108 Combine like terms: 2.916666667 + 0.6267361108 = 3.5434027778 0.6267361108 + -1.583333333y + y2 = 3.5434027778 Factor a perfect square on the left side: (y + -0.7916666665)(y + -0.7916666665) = 3.5434027778 Calculate the square root of the right side: 1.882392833 Break this problem into two subproblems by setting (y + -0.7916666665) equal to 1.882392833 and -1.882392833.Subproblem 1
y + -0.7916666665 = 1.882392833 Simplifying y + -0.7916666665 = 1.882392833 Reorder the terms: -0.7916666665 + y = 1.882392833 Solving -0.7916666665 + y = 1.882392833 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.7916666665' to each side of the equation. -0.7916666665 + 0.7916666665 + y = 1.882392833 + 0.7916666665 Combine like terms: -0.7916666665 + 0.7916666665 = 0.0000000000 0.0000000000 + y = 1.882392833 + 0.7916666665 y = 1.882392833 + 0.7916666665 Combine like terms: 1.882392833 + 0.7916666665 = 2.6740594995 y = 2.6740594995 Simplifying y = 2.6740594995Subproblem 2
y + -0.7916666665 = -1.882392833 Simplifying y + -0.7916666665 = -1.882392833 Reorder the terms: -0.7916666665 + y = -1.882392833 Solving -0.7916666665 + y = -1.882392833 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.7916666665' to each side of the equation. -0.7916666665 + 0.7916666665 + y = -1.882392833 + 0.7916666665 Combine like terms: -0.7916666665 + 0.7916666665 = 0.0000000000 0.0000000000 + y = -1.882392833 + 0.7916666665 y = -1.882392833 + 0.7916666665 Combine like terms: -1.882392833 + 0.7916666665 = -1.0907261665 y = -1.0907261665 Simplifying y = -1.0907261665Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.6740594995, -1.0907261665}
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