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Simplifying 6y(y + -9) = (7 + 5y) Reorder the terms: 6y(-9 + y) = (7 + 5y) (-9 * 6y + y * 6y) = (7 + 5y) (-54y + 6y2) = (7 + 5y) Remove parenthesis around (7 + 5y) -54y + 6y2 = 7 + 5y Solving -54y + 6y2 = 7 + 5y Solving for variable 'y'. Reorder the terms: -7 + -54y + -5y + 6y2 = 7 + 5y + -7 + -5y Combine like terms: -54y + -5y = -59y -7 + -59y + 6y2 = 7 + 5y + -7 + -5y Reorder the terms: -7 + -59y + 6y2 = 7 + -7 + 5y + -5y Combine like terms: 7 + -7 = 0 -7 + -59y + 6y2 = 0 + 5y + -5y -7 + -59y + 6y2 = 5y + -5y Combine like terms: 5y + -5y = 0 -7 + -59y + 6y2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1.166666667 + -9.833333333y + y2 = 0 Move the constant term to the right: Add '1.166666667' to each side of the equation. -1.166666667 + -9.833333333y + 1.166666667 + y2 = 0 + 1.166666667 Reorder the terms: -1.166666667 + 1.166666667 + -9.833333333y + y2 = 0 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + -9.833333333y + y2 = 0 + 1.166666667 -9.833333333y + y2 = 0 + 1.166666667 Combine like terms: 0 + 1.166666667 = 1.166666667 -9.833333333y + y2 = 1.166666667 The y term is -9.833333333y. Take half its coefficient (-4.916666667). Square it (24.17361111) and add it to both sides. Add '24.17361111' to each side of the equation. -9.833333333y + 24.17361111 + y2 = 1.166666667 + 24.17361111 Reorder the terms: 24.17361111 + -9.833333333y + y2 = 1.166666667 + 24.17361111 Combine like terms: 1.166666667 + 24.17361111 = 25.340277777 24.17361111 + -9.833333333y + y2 = 25.340277777 Factor a perfect square on the left side: (y + -4.916666667)(y + -4.916666667) = 25.340277777 Calculate the square root of the right side: 5.03391277 Break this problem into two subproblems by setting (y + -4.916666667) equal to 5.03391277 and -5.03391277.Subproblem 1
y + -4.916666667 = 5.03391277 Simplifying y + -4.916666667 = 5.03391277 Reorder the terms: -4.916666667 + y = 5.03391277 Solving -4.916666667 + y = 5.03391277 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4.916666667' to each side of the equation. -4.916666667 + 4.916666667 + y = 5.03391277 + 4.916666667 Combine like terms: -4.916666667 + 4.916666667 = 0.000000000 0.000000000 + y = 5.03391277 + 4.916666667 y = 5.03391277 + 4.916666667 Combine like terms: 5.03391277 + 4.916666667 = 9.950579437 y = 9.950579437 Simplifying y = 9.950579437Subproblem 2
y + -4.916666667 = -5.03391277 Simplifying y + -4.916666667 = -5.03391277 Reorder the terms: -4.916666667 + y = -5.03391277 Solving -4.916666667 + y = -5.03391277 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4.916666667' to each side of the equation. -4.916666667 + 4.916666667 + y = -5.03391277 + 4.916666667 Combine like terms: -4.916666667 + 4.916666667 = 0.000000000 0.000000000 + y = -5.03391277 + 4.916666667 y = -5.03391277 + 4.916666667 Combine like terms: -5.03391277 + 4.916666667 = -0.117246103 y = -0.117246103 Simplifying y = -0.117246103Solution
The solution to the problem is based on the solutions from the subproblems. y = {9.950579437, -0.117246103}
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