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Simplifying 3y2 + -57y + 8 = 0 Reorder the terms: 8 + -57y + 3y2 = 0 Solving 8 + -57y + 3y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2.666666667 + -19y + y2 = 0 Move the constant term to the right: Add '-2.666666667' to each side of the equation. 2.666666667 + -19y + -2.666666667 + y2 = 0 + -2.666666667 Reorder the terms: 2.666666667 + -2.666666667 + -19y + y2 = 0 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + -19y + y2 = 0 + -2.666666667 -19y + y2 = 0 + -2.666666667 Combine like terms: 0 + -2.666666667 = -2.666666667 -19y + y2 = -2.666666667 The y term is -19y. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19y + 90.25 + y2 = -2.666666667 + 90.25 Reorder the terms: 90.25 + -19y + y2 = -2.666666667 + 90.25 Combine like terms: -2.666666667 + 90.25 = 87.583333333 90.25 + -19y + y2 = 87.583333333 Factor a perfect square on the left side: (y + -9.5)(y + -9.5) = 87.583333333 Calculate the square root of the right side: 9.358596761 Break this problem into two subproblems by setting (y + -9.5) equal to 9.358596761 and -9.358596761.Subproblem 1
y + -9.5 = 9.358596761 Simplifying y + -9.5 = 9.358596761 Reorder the terms: -9.5 + y = 9.358596761 Solving -9.5 + y = 9.358596761 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + y = 9.358596761 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + y = 9.358596761 + 9.5 y = 9.358596761 + 9.5 Combine like terms: 9.358596761 + 9.5 = 18.858596761 y = 18.858596761 Simplifying y = 18.858596761Subproblem 2
y + -9.5 = -9.358596761 Simplifying y + -9.5 = -9.358596761 Reorder the terms: -9.5 + y = -9.358596761 Solving -9.5 + y = -9.358596761 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + y = -9.358596761 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + y = -9.358596761 + 9.5 y = -9.358596761 + 9.5 Combine like terms: -9.358596761 + 9.5 = 0.141403239 y = 0.141403239 Simplifying y = 0.141403239Solution
The solution to the problem is based on the solutions from the subproblems. y = {18.858596761, 0.141403239}
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