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Simplifying y2 + -10y = 37 Reorder the terms: -10y + y2 = 37 Solving -10y + y2 = 37 Solving for variable 'y'. Reorder the terms: -37 + -10y + y2 = 37 + -37 Combine like terms: 37 + -37 = 0 -37 + -10y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '37' to each side of the equation. -37 + -10y + 37 + y2 = 0 + 37 Reorder the terms: -37 + 37 + -10y + y2 = 0 + 37 Combine like terms: -37 + 37 = 0 0 + -10y + y2 = 0 + 37 -10y + y2 = 0 + 37 Combine like terms: 0 + 37 = 37 -10y + y2 = 37 The y term is -10y. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10y + 25 + y2 = 37 + 25 Reorder the terms: 25 + -10y + y2 = 37 + 25 Combine like terms: 37 + 25 = 62 25 + -10y + y2 = 62 Factor a perfect square on the left side: (y + -5)(y + -5) = 62 Calculate the square root of the right side: 7.874007874 Break this problem into two subproblems by setting (y + -5) equal to 7.874007874 and -7.874007874.Subproblem 1
y + -5 = 7.874007874 Simplifying y + -5 = 7.874007874 Reorder the terms: -5 + y = 7.874007874 Solving -5 + y = 7.874007874 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + y = 7.874007874 + 5 Combine like terms: -5 + 5 = 0 0 + y = 7.874007874 + 5 y = 7.874007874 + 5 Combine like terms: 7.874007874 + 5 = 12.874007874 y = 12.874007874 Simplifying y = 12.874007874Subproblem 2
y + -5 = -7.874007874 Simplifying y + -5 = -7.874007874 Reorder the terms: -5 + y = -7.874007874 Solving -5 + y = -7.874007874 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + y = -7.874007874 + 5 Combine like terms: -5 + 5 = 0 0 + y = -7.874007874 + 5 y = -7.874007874 + 5 Combine like terms: -7.874007874 + 5 = -2.874007874 y = -2.874007874 Simplifying y = -2.874007874Solution
The solution to the problem is based on the solutions from the subproblems. y = {12.874007874, -2.874007874}
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