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Simplifying 4y + -3y(y + -5) + 2 = 5 Reorder the terms: 4y + -3y(-5 + y) + 2 = 5 4y + (-5 * -3y + y * -3y) + 2 = 5 4y + (15y + -3y2) + 2 = 5 Reorder the terms: 2 + 4y + 15y + -3y2 = 5 Combine like terms: 4y + 15y = 19y 2 + 19y + -3y2 = 5 Solving 2 + 19y + -3y2 = 5 Solving for variable 'y'. Reorder the terms: 2 + -5 + 19y + -3y2 = 5 + -5 Combine like terms: 2 + -5 = -3 -3 + 19y + -3y2 = 5 + -5 Combine like terms: 5 + -5 = 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 = 9.02777778 10.02777778 + -6.333333333y + y2 = 9.02777778 Factor a perfect square on the left side: (y + -3.166666667)(y + -3.166666667) = 9.02777778 Calculate the square root of the right side: 3.004626063 Break this problem into two subproblems by setting (y + -3.166666667) equal to 3.004626063 and -3.004626063.Subproblem 1
y + -3.166666667 = 3.004626063 Simplifying y + -3.166666667 = 3.004626063 Reorder the terms: -3.166666667 + y = 3.004626063 Solving -3.166666667 + y = 3.004626063 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 = 3.004626063 + 3.166666667 Combine like terms: -3.166666667 + 3.166666667 = 0.000000000 0.000000000 + y = 3.004626063 + 3.166666667 y = 3.004626063 + 3.166666667 Combine like terms: 3.004626063 + 3.166666667 = 6.17129273 y = 6.17129273 Simplifying y = 6.17129273Subproblem 2
y + -3.166666667 = -3.004626063 Simplifying y + -3.166666667 = -3.004626063 Reorder the terms: -3.166666667 + y = -3.004626063 Solving -3.166666667 + y = -3.004626063 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 = -3.004626063 + 3.166666667 Combine like terms: -3.166666667 + 3.166666667 = 0.000000000 0.000000000 + y = -3.004626063 + 3.166666667 y = -3.004626063 + 3.166666667 Combine like terms: -3.004626063 + 3.166666667 = 0.162040604 y = 0.162040604 Simplifying y = 0.162040604Solution
The solution to the problem is based on the solutions from the subproblems. y = {6.17129273, 0.162040604}
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