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Simplifying -9y(y + 7) + -6(y + -3) = 0 Reorder the terms: -9y(7 + y) + -6(y + -3) = 0 (7 * -9y + y * -9y) + -6(y + -3) = 0 (-63y + -9y2) + -6(y + -3) = 0 Reorder the terms: -63y + -9y2 + -6(-3 + y) = 0 -63y + -9y2 + (-3 * -6 + y * -6) = 0 -63y + -9y2 + (18 + -6y) = 0 Reorder the terms: 18 + -63y + -6y + -9y2 = 0 Combine like terms: -63y + -6y = -69y 18 + -69y + -9y2 = 0 Solving 18 + -69y + -9y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '3'. 3(6 + -23y + -3y2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(6 + -23y + -3y2)' equal to zero and attempt to solve: Simplifying 6 + -23y + -3y2 = 0 Solving 6 + -23y + -3y2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -2 + 7.666666667y + y2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 7.666666667y + 2 + y2 = 0 + 2 Reorder the terms: -2 + 2 + 7.666666667y + y2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 7.666666667y + y2 = 0 + 2 7.666666667y + y2 = 0 + 2 Combine like terms: 0 + 2 = 2 7.666666667y + y2 = 2 The y term is 7.666666667y. Take half its coefficient (3.833333334). Square it (14.69444445) and add it to both sides. Add '14.69444445' to each side of the equation. 7.666666667y + 14.69444445 + y2 = 2 + 14.69444445 Reorder the terms: 14.69444445 + 7.666666667y + y2 = 2 + 14.69444445 Combine like terms: 2 + 14.69444445 = 16.69444445 14.69444445 + 7.666666667y + y2 = 16.69444445 Factor a perfect square on the left side: (y + 3.833333334)(y + 3.833333334) = 16.69444445 Calculate the square root of the right side: 4.085883558 Break this problem into two subproblems by setting (y + 3.833333334) equal to 4.085883558 and -4.085883558.Subproblem 1
y + 3.833333334 = 4.085883558 Simplifying y + 3.833333334 = 4.085883558 Reorder the terms: 3.833333334 + y = 4.085883558 Solving 3.833333334 + y = 4.085883558 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3.833333334' to each side of the equation. 3.833333334 + -3.833333334 + y = 4.085883558 + -3.833333334 Combine like terms: 3.833333334 + -3.833333334 = 0.000000000 0.000000000 + y = 4.085883558 + -3.833333334 y = 4.085883558 + -3.833333334 Combine like terms: 4.085883558 + -3.833333334 = 0.252550224 y = 0.252550224 Simplifying y = 0.252550224Subproblem 2
y + 3.833333334 = -4.085883558 Simplifying y + 3.833333334 = -4.085883558 Reorder the terms: 3.833333334 + y = -4.085883558 Solving 3.833333334 + y = -4.085883558 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3.833333334' to each side of the equation. 3.833333334 + -3.833333334 + y = -4.085883558 + -3.833333334 Combine like terms: 3.833333334 + -3.833333334 = 0.000000000 0.000000000 + y = -4.085883558 + -3.833333334 y = -4.085883558 + -3.833333334 Combine like terms: -4.085883558 + -3.833333334 = -7.919216892 y = -7.919216892 Simplifying y = -7.919216892Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.252550224, -7.919216892}Solution
y = {0.252550224, -7.919216892}
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