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Simplifying (7 + -2y) + 5y(9 + -3y) = 0 Remove parenthesis around (7 + -2y) 7 + -2y + 5y(9 + -3y) = 0 7 + -2y + (9 * 5y + -3y * 5y) = 0 7 + -2y + (45y + -15y2) = 0 Combine like terms: -2y + 45y = 43y 7 + 43y + -15y2 = 0 Solving 7 + 43y + -15y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by -15 the coefficient of the squared term: Divide each side by '-15'. -0.4666666667 + -2.866666667y + y2 = 0 Move the constant term to the right: Add '0.4666666667' to each side of the equation. -0.4666666667 + -2.866666667y + 0.4666666667 + y2 = 0 + 0.4666666667 Reorder the terms: -0.4666666667 + 0.4666666667 + -2.866666667y + y2 = 0 + 0.4666666667 Combine like terms: -0.4666666667 + 0.4666666667 = 0.0000000000 0.0000000000 + -2.866666667y + y2 = 0 + 0.4666666667 -2.866666667y + y2 = 0 + 0.4666666667 Combine like terms: 0 + 0.4666666667 = 0.4666666667 -2.866666667y + y2 = 0.4666666667 The y term is -2.866666667y. Take half its coefficient (-1.433333334). Square it (2.054444446) and add it to both sides. Add '2.054444446' to each side of the equation. -2.866666667y + 2.054444446 + y2 = 0.4666666667 + 2.054444446 Reorder the terms: 2.054444446 + -2.866666667y + y2 = 0.4666666667 + 2.054444446 Combine like terms: 0.4666666667 + 2.054444446 = 2.5211111127 2.054444446 + -2.866666667y + y2 = 2.5211111127 Factor a perfect square on the left side: (y + -1.433333334)(y + -1.433333334) = 2.5211111127 Calculate the square root of the right side: 1.587800716 Break this problem into two subproblems by setting (y + -1.433333334) equal to 1.587800716 and -1.587800716.Subproblem 1
y + -1.433333334 = 1.587800716 Simplifying y + -1.433333334 = 1.587800716 Reorder the terms: -1.433333334 + y = 1.587800716 Solving -1.433333334 + y = 1.587800716 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.433333334' to each side of the equation. -1.433333334 + 1.433333334 + y = 1.587800716 + 1.433333334 Combine like terms: -1.433333334 + 1.433333334 = 0.000000000 0.000000000 + y = 1.587800716 + 1.433333334 y = 1.587800716 + 1.433333334 Combine like terms: 1.587800716 + 1.433333334 = 3.02113405 y = 3.02113405 Simplifying y = 3.02113405Subproblem 2
y + -1.433333334 = -1.587800716 Simplifying y + -1.433333334 = -1.587800716 Reorder the terms: -1.433333334 + y = -1.587800716 Solving -1.433333334 + y = -1.587800716 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.433333334' to each side of the equation. -1.433333334 + 1.433333334 + y = -1.587800716 + 1.433333334 Combine like terms: -1.433333334 + 1.433333334 = 0.000000000 0.000000000 + y = -1.587800716 + 1.433333334 y = -1.587800716 + 1.433333334 Combine like terms: -1.587800716 + 1.433333334 = -0.154467382 y = -0.154467382 Simplifying y = -0.154467382Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.02113405, -0.154467382}
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