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Simplifying y2 + y + -150 = 0 Reorder the terms: -150 + y + y2 = 0 Solving -150 + y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '150' to each side of the equation. -150 + y + 150 + y2 = 0 + 150 Reorder the terms: -150 + 150 + y + y2 = 0 + 150 Combine like terms: -150 + 150 = 0 0 + y + y2 = 0 + 150 y + y2 = 0 + 150 Combine like terms: 0 + 150 = 150 y + y2 = 150 The y term is y. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. y + 0.25 + y2 = 150 + 0.25 Reorder the terms: 0.25 + y + y2 = 150 + 0.25 Combine like terms: 150 + 0.25 = 150.25 0.25 + y + y2 = 150.25 Factor a perfect square on the left side: (y + 0.5)(y + 0.5) = 150.25 Calculate the square root of the right side: 12.257650672 Break this problem into two subproblems by setting (y + 0.5) equal to 12.257650672 and -12.257650672.Subproblem 1
y + 0.5 = 12.257650672 Simplifying y + 0.5 = 12.257650672 Reorder the terms: 0.5 + y = 12.257650672 Solving 0.5 + y = 12.257650672 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = 12.257650672 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = 12.257650672 + -0.5 y = 12.257650672 + -0.5 Combine like terms: 12.257650672 + -0.5 = 11.757650672 y = 11.757650672 Simplifying y = 11.757650672Subproblem 2
y + 0.5 = -12.257650672 Simplifying y + 0.5 = -12.257650672 Reorder the terms: 0.5 + y = -12.257650672 Solving 0.5 + y = -12.257650672 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = -12.257650672 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = -12.257650672 + -0.5 y = -12.257650672 + -0.5 Combine like terms: -12.257650672 + -0.5 = -12.757650672 y = -12.757650672 Simplifying y = -12.757650672Solution
The solution to the problem is based on the solutions from the subproblems. y = {11.757650672, -12.757650672}
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