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Simplifying -39 = 5(y + -7) * 7y Reorder the terms: -39 = 5(-7 + y) * 7y Reorder the terms for easier multiplication: -39 = 5 * 7y(-7 + y) Multiply 5 * 7 -39 = 35y(-7 + y) -39 = (-7 * 35y + y * 35y) -39 = (-245y + 35y2) Solving -39 = -245y + 35y2 Solving for variable 'y'. Reorder the terms: -39 + 245y + -35y2 = -245y + 245y + 35y2 + -35y2 Combine like terms: -245y + 245y = 0 -39 + 245y + -35y2 = 0 + 35y2 + -35y2 -39 + 245y + -35y2 = 35y2 + -35y2 Combine like terms: 35y2 + -35y2 = 0 -39 + 245y + -35y2 = 0 Begin completing the square. Divide all terms by -35 the coefficient of the squared term: Divide each side by '-35'. 1.114285714 + -7y + y2 = 0 Move the constant term to the right: Add '-1.114285714' to each side of the equation. 1.114285714 + -7y + -1.114285714 + y2 = 0 + -1.114285714 Reorder the terms: 1.114285714 + -1.114285714 + -7y + y2 = 0 + -1.114285714 Combine like terms: 1.114285714 + -1.114285714 = 0.000000000 0.000000000 + -7y + y2 = 0 + -1.114285714 -7y + y2 = 0 + -1.114285714 Combine like terms: 0 + -1.114285714 = -1.114285714 -7y + y2 = -1.114285714 The y term is -7y. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7y + 12.25 + y2 = -1.114285714 + 12.25 Reorder the terms: 12.25 + -7y + y2 = -1.114285714 + 12.25 Combine like terms: -1.114285714 + 12.25 = 11.135714286 12.25 + -7y + y2 = 11.135714286 Factor a perfect square on the left side: (y + -3.5)(y + -3.5) = 11.135714286 Calculate the square root of the right side: 3.337021769 Break this problem into two subproblems by setting (y + -3.5) equal to 3.337021769 and -3.337021769.Subproblem 1
y + -3.5 = 3.337021769 Simplifying y + -3.5 = 3.337021769 Reorder the terms: -3.5 + y = 3.337021769 Solving -3.5 + y = 3.337021769 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + y = 3.337021769 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + y = 3.337021769 + 3.5 y = 3.337021769 + 3.5 Combine like terms: 3.337021769 + 3.5 = 6.837021769 y = 6.837021769 Simplifying y = 6.837021769Subproblem 2
y + -3.5 = -3.337021769 Simplifying y + -3.5 = -3.337021769 Reorder the terms: -3.5 + y = -3.337021769 Solving -3.5 + y = -3.337021769 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + y = -3.337021769 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + y = -3.337021769 + 3.5 y = -3.337021769 + 3.5 Combine like terms: -3.337021769 + 3.5 = 0.162978231 y = 0.162978231 Simplifying y = 0.162978231Solution
The solution to the problem is based on the solutions from the subproblems. y = {6.837021769, 0.162978231}
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