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Simplifying y + 10 + y2 + -2 = 21 Reorder the terms: 10 + -2 + y + y2 = 21 Combine like terms: 10 + -2 = 8 8 + y + y2 = 21 Solving 8 + y + y2 = 21 Solving for variable 'y'. Reorder the terms: 8 + -21 + y + y2 = 21 + -21 Combine like terms: 8 + -21 = -13 -13 + y + y2 = 21 + -21 Combine like terms: 21 + -21 = 0 -13 + y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + y + 13 + y2 = 0 + 13 Reorder the terms: -13 + 13 + y + y2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + y + y2 = 0 + 13 y + y2 = 0 + 13 Combine like terms: 0 + 13 = 13 y + y2 = 13 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 = 13 + 0.25 Reorder the terms: 0.25 + y + y2 = 13 + 0.25 Combine like terms: 13 + 0.25 = 13.25 0.25 + y + y2 = 13.25 Factor a perfect square on the left side: (y + 0.5)(y + 0.5) = 13.25 Calculate the square root of the right side: 3.640054945 Break this problem into two subproblems by setting (y + 0.5) equal to 3.640054945 and -3.640054945.Subproblem 1
y + 0.5 = 3.640054945 Simplifying y + 0.5 = 3.640054945 Reorder the terms: 0.5 + y = 3.640054945 Solving 0.5 + y = 3.640054945 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 = 3.640054945 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = 3.640054945 + -0.5 y = 3.640054945 + -0.5 Combine like terms: 3.640054945 + -0.5 = 3.140054945 y = 3.140054945 Simplifying y = 3.140054945Subproblem 2
y + 0.5 = -3.640054945 Simplifying y + 0.5 = -3.640054945 Reorder the terms: 0.5 + y = -3.640054945 Solving 0.5 + y = -3.640054945 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 = -3.640054945 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = -3.640054945 + -0.5 y = -3.640054945 + -0.5 Combine like terms: -3.640054945 + -0.5 = -4.140054945 y = -4.140054945 Simplifying y = -4.140054945Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.140054945, -4.140054945}
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