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Simplifying x2 + -63x + 60 = 0 Reorder the terms: 60 + -63x + x2 = 0 Solving 60 + -63x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-60' to each side of the equation. 60 + -63x + -60 + x2 = 0 + -60 Reorder the terms: 60 + -60 + -63x + x2 = 0 + -60 Combine like terms: 60 + -60 = 0 0 + -63x + x2 = 0 + -60 -63x + x2 = 0 + -60 Combine like terms: 0 + -60 = -60 -63x + x2 = -60 The x term is -63x. Take half its coefficient (-31.5). Square it (992.25) and add it to both sides. Add '992.25' to each side of the equation. -63x + 992.25 + x2 = -60 + 992.25 Reorder the terms: 992.25 + -63x + x2 = -60 + 992.25 Combine like terms: -60 + 992.25 = 932.25 992.25 + -63x + x2 = 932.25 Factor a perfect square on the left side: (x + -31.5)(x + -31.5) = 932.25 Calculate the square root of the right side: 30.532769282 Break this problem into two subproblems by setting (x + -31.5) equal to 30.532769282 and -30.532769282.Subproblem 1
x + -31.5 = 30.532769282 Simplifying x + -31.5 = 30.532769282 Reorder the terms: -31.5 + x = 30.532769282 Solving -31.5 + x = 30.532769282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '31.5' to each side of the equation. -31.5 + 31.5 + x = 30.532769282 + 31.5 Combine like terms: -31.5 + 31.5 = 0.0 0.0 + x = 30.532769282 + 31.5 x = 30.532769282 + 31.5 Combine like terms: 30.532769282 + 31.5 = 62.032769282 x = 62.032769282 Simplifying x = 62.032769282Subproblem 2
x + -31.5 = -30.532769282 Simplifying x + -31.5 = -30.532769282 Reorder the terms: -31.5 + x = -30.532769282 Solving -31.5 + x = -30.532769282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '31.5' to each side of the equation. -31.5 + 31.5 + x = -30.532769282 + 31.5 Combine like terms: -31.5 + 31.5 = 0.0 0.0 + x = -30.532769282 + 31.5 x = -30.532769282 + 31.5 Combine like terms: -30.532769282 + 31.5 = 0.967230718 x = 0.967230718 Simplifying x = 0.967230718Solution
The solution to the problem is based on the solutions from the subproblems. x = {62.032769282, 0.967230718}
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