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Simplifying y2 + -1y + -110 = 7 Reorder the terms: -110 + -1y + y2 = 7 Solving -110 + -1y + y2 = 7 Solving for variable 'y'. Reorder the terms: -110 + -7 + -1y + y2 = 7 + -7 Combine like terms: -110 + -7 = -117 -117 + -1y + y2 = 7 + -7 Combine like terms: 7 + -7 = 0 -117 + -1y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '117' to each side of the equation. -117 + -1y + 117 + y2 = 0 + 117 Reorder the terms: -117 + 117 + -1y + y2 = 0 + 117 Combine like terms: -117 + 117 = 0 0 + -1y + y2 = 0 + 117 -1y + y2 = 0 + 117 Combine like terms: 0 + 117 = 117 -1y + y2 = 117 The y term is -1y. 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. -1y + 0.25 + y2 = 117 + 0.25 Reorder the terms: 0.25 + -1y + y2 = 117 + 0.25 Combine like terms: 117 + 0.25 = 117.25 0.25 + -1y + y2 = 117.25 Factor a perfect square on the left side: (y + -0.5)(y + -0.5) = 117.25 Calculate the square root of the right side: 10.828203914 Break this problem into two subproblems by setting (y + -0.5) equal to 10.828203914 and -10.828203914.Subproblem 1
y + -0.5 = 10.828203914 Simplifying y + -0.5 = 10.828203914 Reorder the terms: -0.5 + y = 10.828203914 Solving -0.5 + y = 10.828203914 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 = 10.828203914 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = 10.828203914 + 0.5 y = 10.828203914 + 0.5 Combine like terms: 10.828203914 + 0.5 = 11.328203914 y = 11.328203914 Simplifying y = 11.328203914Subproblem 2
y + -0.5 = -10.828203914 Simplifying y + -0.5 = -10.828203914 Reorder the terms: -0.5 + y = -10.828203914 Solving -0.5 + y = -10.828203914 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 = -10.828203914 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = -10.828203914 + 0.5 y = -10.828203914 + 0.5 Combine like terms: -10.828203914 + 0.5 = -10.328203914 y = -10.328203914 Simplifying y = -10.328203914Solution
The solution to the problem is based on the solutions from the subproblems. y = {11.328203914, -10.328203914}
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