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Simplifying (6y2 + -19y + -15) = 0 Reorder the terms: (-15 + -19y + 6y2) = 0 Remove parenthesis around (-15 + -19y + 6y2) -15 + -19y + 6y2 = 0 Solving -15 + -19y + 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'. -2.5 + -3.166666667y + y2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -3.166666667y + 2.5 + y2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -3.166666667y + y2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -3.166666667y + y2 = 0 + 2.5 -3.166666667y + y2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -3.166666667y + y2 = 2.5 The y term is -3.166666667y. Take half its coefficient (-1.583333334). Square it (2.506944447) and add it to both sides. Add '2.506944447' to each side of the equation. -3.166666667y + 2.506944447 + y2 = 2.5 + 2.506944447 Reorder the terms: 2.506944447 + -3.166666667y + y2 = 2.5 + 2.506944447 Combine like terms: 2.5 + 2.506944447 = 5.006944447 2.506944447 + -3.166666667y + y2 = 5.006944447 Factor a perfect square on the left side: (y + -1.583333334)(y + -1.583333334) = 5.006944447 Calculate the square root of the right side: 2.237620264 Break this problem into two subproblems by setting (y + -1.583333334) equal to 2.237620264 and -2.237620264.Subproblem 1
y + -1.583333334 = 2.237620264 Simplifying y + -1.583333334 = 2.237620264 Reorder the terms: -1.583333334 + y = 2.237620264 Solving -1.583333334 + y = 2.237620264 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.583333334' to each side of the equation. -1.583333334 + 1.583333334 + y = 2.237620264 + 1.583333334 Combine like terms: -1.583333334 + 1.583333334 = 0.000000000 0.000000000 + y = 2.237620264 + 1.583333334 y = 2.237620264 + 1.583333334 Combine like terms: 2.237620264 + 1.583333334 = 3.820953598 y = 3.820953598 Simplifying y = 3.820953598Subproblem 2
y + -1.583333334 = -2.237620264 Simplifying y + -1.583333334 = -2.237620264 Reorder the terms: -1.583333334 + y = -2.237620264 Solving -1.583333334 + y = -2.237620264 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.583333334' to each side of the equation. -1.583333334 + 1.583333334 + y = -2.237620264 + 1.583333334 Combine like terms: -1.583333334 + 1.583333334 = 0.000000000 0.000000000 + y = -2.237620264 + 1.583333334 y = -2.237620264 + 1.583333334 Combine like terms: -2.237620264 + 1.583333334 = -0.65428693 y = -0.65428693 Simplifying y = -0.65428693Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.820953598, -0.65428693}
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