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Simplifying 7(2y + -1) + 3y = -3y(y + 2) + 9 Reorder the terms: 7(-1 + 2y) + 3y = -3y(y + 2) + 9 (-1 * 7 + 2y * 7) + 3y = -3y(y + 2) + 9 (-7 + 14y) + 3y = -3y(y + 2) + 9 Combine like terms: 14y + 3y = 17y -7 + 17y = -3y(y + 2) + 9 Reorder the terms: -7 + 17y = -3y(2 + y) + 9 -7 + 17y = (2 * -3y + y * -3y) + 9 -7 + 17y = (-6y + -3y2) + 9 Reorder the terms: -7 + 17y = 9 + -6y + -3y2 Solving -7 + 17y = 9 + -6y + -3y2 Solving for variable 'y'. Reorder the terms: -7 + -9 + 17y + 6y + 3y2 = 9 + -6y + -3y2 + -9 + 6y + 3y2 Combine like terms: -7 + -9 = -16 -16 + 17y + 6y + 3y2 = 9 + -6y + -3y2 + -9 + 6y + 3y2 Combine like terms: 17y + 6y = 23y -16 + 23y + 3y2 = 9 + -6y + -3y2 + -9 + 6y + 3y2 Reorder the terms: -16 + 23y + 3y2 = 9 + -9 + -6y + 6y + -3y2 + 3y2 Combine like terms: 9 + -9 = 0 -16 + 23y + 3y2 = 0 + -6y + 6y + -3y2 + 3y2 -16 + 23y + 3y2 = -6y + 6y + -3y2 + 3y2 Combine like terms: -6y + 6y = 0 -16 + 23y + 3y2 = 0 + -3y2 + 3y2 -16 + 23y + 3y2 = -3y2 + 3y2 Combine like terms: -3y2 + 3y2 = 0 -16 + 23y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -5.333333333 + 7.666666667y + y2 = 0 Move the constant term to the right: Add '5.333333333' to each side of the equation. -5.333333333 + 7.666666667y + 5.333333333 + y2 = 0 + 5.333333333 Reorder the terms: -5.333333333 + 5.333333333 + 7.666666667y + y2 = 0 + 5.333333333 Combine like terms: -5.333333333 + 5.333333333 = 0.000000000 0.000000000 + 7.666666667y + y2 = 0 + 5.333333333 7.666666667y + y2 = 0 + 5.333333333 Combine like terms: 0 + 5.333333333 = 5.333333333 7.666666667y + y2 = 5.333333333 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 = 5.333333333 + 14.69444445 Reorder the terms: 14.69444445 + 7.666666667y + y2 = 5.333333333 + 14.69444445 Combine like terms: 5.333333333 + 14.69444445 = 20.027777783 14.69444445 + 7.666666667y + y2 = 20.027777783 Factor a perfect square on the left side: (y + 3.833333334)(y + 3.833333334) = 20.027777783 Calculate the square root of the right side: 4.475240528 Break this problem into two subproblems by setting (y + 3.833333334) equal to 4.475240528 and -4.475240528.Subproblem 1
y + 3.833333334 = 4.475240528 Simplifying y + 3.833333334 = 4.475240528 Reorder the terms: 3.833333334 + y = 4.475240528 Solving 3.833333334 + y = 4.475240528 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 = 4.475240528 + -3.833333334 Combine like terms: 3.833333334 + -3.833333334 = 0.000000000 0.000000000 + y = 4.475240528 + -3.833333334 y = 4.475240528 + -3.833333334 Combine like terms: 4.475240528 + -3.833333334 = 0.641907194 y = 0.641907194 Simplifying y = 0.641907194Subproblem 2
y + 3.833333334 = -4.475240528 Simplifying y + 3.833333334 = -4.475240528 Reorder the terms: 3.833333334 + y = -4.475240528 Solving 3.833333334 + y = -4.475240528 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 = -4.475240528 + -3.833333334 Combine like terms: 3.833333334 + -3.833333334 = 0.000000000 0.000000000 + y = -4.475240528 + -3.833333334 y = -4.475240528 + -3.833333334 Combine like terms: -4.475240528 + -3.833333334 = -8.308573862 y = -8.308573862 Simplifying y = -8.308573862Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.641907194, -8.308573862}
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