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Simplifying 2y + 3 = 3y(y + 7) Reorder the terms: 3 + 2y = 3y(y + 7) Reorder the terms: 3 + 2y = 3y(7 + y) 3 + 2y = (7 * 3y + y * 3y) 3 + 2y = (21y + 3y2) Solving 3 + 2y = 21y + 3y2 Solving for variable 'y'. Combine like terms: 2y + -21y = -19y 3 + -19y + -3y2 = 21y + 3y2 + -21y + -3y2 Reorder the terms: 3 + -19y + -3y2 = 21y + -21y + 3y2 + -3y2 Combine like terms: 21y + -21y = 0 3 + -19y + -3y2 = 0 + 3y2 + -3y2 3 + -19y + -3y2 = 3y2 + -3y2 Combine like terms: 3y2 + -3y2 = 0 3 + -19y + -3y2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -1 + 6.333333333y + y2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 6.333333333y + 1 + y2 = 0 + 1 Reorder the terms: -1 + 1 + 6.333333333y + y2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 6.333333333y + y2 = 0 + 1 6.333333333y + y2 = 0 + 1 Combine like terms: 0 + 1 = 1 6.333333333y + y2 = 1 The y term is 6.333333333y. Take half its coefficient (3.166666667). Square it (10.02777778) and add it to both sides. Add '10.02777778' to each side of the equation. 6.333333333y + 10.02777778 + y2 = 1 + 10.02777778 Reorder the terms: 10.02777778 + 6.333333333y + y2 = 1 + 10.02777778 Combine like terms: 1 + 10.02777778 = 11.02777778 10.02777778 + 6.333333333y + y2 = 11.02777778 Factor a perfect square on the left side: (y + 3.166666667)(y + 3.166666667) = 11.02777778 Calculate the square root of the right side: 3.320809808 Break this problem into two subproblems by setting (y + 3.166666667) equal to 3.320809808 and -3.320809808.Subproblem 1
y + 3.166666667 = 3.320809808 Simplifying y + 3.166666667 = 3.320809808 Reorder the terms: 3.166666667 + y = 3.320809808 Solving 3.166666667 + y = 3.320809808 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3.166666667' to each side of the equation. 3.166666667 + -3.166666667 + y = 3.320809808 + -3.166666667 Combine like terms: 3.166666667 + -3.166666667 = 0.000000000 0.000000000 + y = 3.320809808 + -3.166666667 y = 3.320809808 + -3.166666667 Combine like terms: 3.320809808 + -3.166666667 = 0.154143141 y = 0.154143141 Simplifying y = 0.154143141Subproblem 2
y + 3.166666667 = -3.320809808 Simplifying y + 3.166666667 = -3.320809808 Reorder the terms: 3.166666667 + y = -3.320809808 Solving 3.166666667 + y = -3.320809808 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3.166666667' to each side of the equation. 3.166666667 + -3.166666667 + y = -3.320809808 + -3.166666667 Combine like terms: 3.166666667 + -3.166666667 = 0.000000000 0.000000000 + y = -3.320809808 + -3.166666667 y = -3.320809808 + -3.166666667 Combine like terms: -3.320809808 + -3.166666667 = -6.487476475 y = -6.487476475 Simplifying y = -6.487476475Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.154143141, -6.487476475}
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