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Simplifying y2 + -4y + -37 = 0 Reorder the terms: -37 + -4y + y2 = 0 Solving -37 + -4y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '37' to each side of the equation. -37 + -4y + 37 + y2 = 0 + 37 Reorder the terms: -37 + 37 + -4y + y2 = 0 + 37 Combine like terms: -37 + 37 = 0 0 + -4y + y2 = 0 + 37 -4y + y2 = 0 + 37 Combine like terms: 0 + 37 = 37 -4y + y2 = 37 The y term is -4y. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4y + 4 + y2 = 37 + 4 Reorder the terms: 4 + -4y + y2 = 37 + 4 Combine like terms: 37 + 4 = 41 4 + -4y + y2 = 41 Factor a perfect square on the left side: (y + -2)(y + -2) = 41 Calculate the square root of the right side: 6.403124237 Break this problem into two subproblems by setting (y + -2) equal to 6.403124237 and -6.403124237.Subproblem 1
y + -2 = 6.403124237 Simplifying y + -2 = 6.403124237 Reorder the terms: -2 + y = 6.403124237 Solving -2 + y = 6.403124237 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = 6.403124237 + 2 Combine like terms: -2 + 2 = 0 0 + y = 6.403124237 + 2 y = 6.403124237 + 2 Combine like terms: 6.403124237 + 2 = 8.403124237 y = 8.403124237 Simplifying y = 8.403124237Subproblem 2
y + -2 = -6.403124237 Simplifying y + -2 = -6.403124237 Reorder the terms: -2 + y = -6.403124237 Solving -2 + y = -6.403124237 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = -6.403124237 + 2 Combine like terms: -2 + 2 = 0 0 + y = -6.403124237 + 2 y = -6.403124237 + 2 Combine like terms: -6.403124237 + 2 = -4.403124237 y = -4.403124237 Simplifying y = -4.403124237Solution
The solution to the problem is based on the solutions from the subproblems. y = {8.403124237, -4.403124237}
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