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Simplifying 3y2 + -2y + -504 = 0 Reorder the terms: -504 + -2y + 3y2 = 0 Solving -504 + -2y + 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'. -168 + -0.6666666667y + y2 = 0 Move the constant term to the right: Add '168' to each side of the equation. -168 + -0.6666666667y + 168 + y2 = 0 + 168 Reorder the terms: -168 + 168 + -0.6666666667y + y2 = 0 + 168 Combine like terms: -168 + 168 = 0 0 + -0.6666666667y + y2 = 0 + 168 -0.6666666667y + y2 = 0 + 168 Combine like terms: 0 + 168 = 168 -0.6666666667y + y2 = 168 The y term is -0.6666666667y. Take half its coefficient (-0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. -0.6666666667y + 0.1111111112 + y2 = 168 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667y + y2 = 168 + 0.1111111112 Combine like terms: 168 + 0.1111111112 = 168.1111111112 0.1111111112 + -0.6666666667y + y2 = 168.1111111112 Factor a perfect square on the left side: (y + -0.3333333334)(y + -0.3333333334) = 168.1111111112 Calculate the square root of the right side: 12.965766893 Break this problem into two subproblems by setting (y + -0.3333333334) equal to 12.965766893 and -12.965766893.Subproblem 1
y + -0.3333333334 = 12.965766893 Simplifying y + -0.3333333334 = 12.965766893 Reorder the terms: -0.3333333334 + y = 12.965766893 Solving -0.3333333334 + y = 12.965766893 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + y = 12.965766893 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + y = 12.965766893 + 0.3333333334 y = 12.965766893 + 0.3333333334 Combine like terms: 12.965766893 + 0.3333333334 = 13.2991002264 y = 13.2991002264 Simplifying y = 13.2991002264Subproblem 2
y + -0.3333333334 = -12.965766893 Simplifying y + -0.3333333334 = -12.965766893 Reorder the terms: -0.3333333334 + y = -12.965766893 Solving -0.3333333334 + y = -12.965766893 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + y = -12.965766893 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + y = -12.965766893 + 0.3333333334 y = -12.965766893 + 0.3333333334 Combine like terms: -12.965766893 + 0.3333333334 = -12.6324335596 y = -12.6324335596 Simplifying y = -12.6324335596Solution
The solution to the problem is based on the solutions from the subproblems. y = {13.2991002264, -12.6324335596}
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