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Simplifying (y2 + -6) + (90) + (y + 1) = 180 Reorder the terms: (-6 + y2) + (90) + (y + 1) = 180 Remove parenthesis around (-6 + y2) -6 + y2 + (90) + (y + 1) = 180 -6 + y2 + 90 + (y + 1) = 180 Reorder the terms: -6 + y2 + 90 + (1 + y) = 180 Remove parenthesis around (1 + y) -6 + y2 + 90 + 1 + y = 180 Reorder the terms: -6 + 90 + 1 + y + y2 = 180 Combine like terms: -6 + 90 = 84 84 + 1 + y + y2 = 180 Combine like terms: 84 + 1 = 85 85 + y + y2 = 180 Solving 85 + y + y2 = 180 Solving for variable 'y'. Reorder the terms: 85 + -180 + y + y2 = 180 + -180 Combine like terms: 85 + -180 = -95 -95 + y + y2 = 180 + -180 Combine like terms: 180 + -180 = 0 -95 + y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '95' to each side of the equation. -95 + y + 95 + y2 = 0 + 95 Reorder the terms: -95 + 95 + y + y2 = 0 + 95 Combine like terms: -95 + 95 = 0 0 + y + y2 = 0 + 95 y + y2 = 0 + 95 Combine like terms: 0 + 95 = 95 y + y2 = 95 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 = 95 + 0.25 Reorder the terms: 0.25 + y + y2 = 95 + 0.25 Combine like terms: 95 + 0.25 = 95.25 0.25 + y + y2 = 95.25 Factor a perfect square on the left side: (y + 0.5)(y + 0.5) = 95.25 Calculate the square root of the right side: 9.759610648 Break this problem into two subproblems by setting (y + 0.5) equal to 9.759610648 and -9.759610648.Subproblem 1
y + 0.5 = 9.759610648 Simplifying y + 0.5 = 9.759610648 Reorder the terms: 0.5 + y = 9.759610648 Solving 0.5 + y = 9.759610648 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 = 9.759610648 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = 9.759610648 + -0.5 y = 9.759610648 + -0.5 Combine like terms: 9.759610648 + -0.5 = 9.259610648 y = 9.259610648 Simplifying y = 9.259610648Subproblem 2
y + 0.5 = -9.759610648 Simplifying y + 0.5 = -9.759610648 Reorder the terms: 0.5 + y = -9.759610648 Solving 0.5 + y = -9.759610648 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 = -9.759610648 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = -9.759610648 + -0.5 y = -9.759610648 + -0.5 Combine like terms: -9.759610648 + -0.5 = -10.259610648 y = -10.259610648 Simplifying y = -10.259610648Solution
The solution to the problem is based on the solutions from the subproblems. y = {9.259610648, -10.259610648}
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