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Simplifying x2 + -21x + -144 = 0 Reorder the terms: -144 + -21x + x2 = 0 Solving -144 + -21x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '144' to each side of the equation. -144 + -21x + 144 + x2 = 0 + 144 Reorder the terms: -144 + 144 + -21x + x2 = 0 + 144 Combine like terms: -144 + 144 = 0 0 + -21x + x2 = 0 + 144 -21x + x2 = 0 + 144 Combine like terms: 0 + 144 = 144 -21x + x2 = 144 The x term is -21x. Take half its coefficient (-10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. -21x + 110.25 + x2 = 144 + 110.25 Reorder the terms: 110.25 + -21x + x2 = 144 + 110.25 Combine like terms: 144 + 110.25 = 254.25 110.25 + -21x + x2 = 254.25 Factor a perfect square on the left side: (x + -10.5)(x + -10.5) = 254.25 Calculate the square root of the right side: 15.945218719 Break this problem into two subproblems by setting (x + -10.5) equal to 15.945218719 and -15.945218719.Subproblem 1
x + -10.5 = 15.945218719 Simplifying x + -10.5 = 15.945218719 Reorder the terms: -10.5 + x = 15.945218719 Solving -10.5 + x = 15.945218719 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = 15.945218719 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = 15.945218719 + 10.5 x = 15.945218719 + 10.5 Combine like terms: 15.945218719 + 10.5 = 26.445218719 x = 26.445218719 Simplifying x = 26.445218719Subproblem 2
x + -10.5 = -15.945218719 Simplifying x + -10.5 = -15.945218719 Reorder the terms: -10.5 + x = -15.945218719 Solving -10.5 + x = -15.945218719 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = -15.945218719 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = -15.945218719 + 10.5 x = -15.945218719 + 10.5 Combine like terms: -15.945218719 + 10.5 = -5.445218719 x = -5.445218719 Simplifying x = -5.445218719Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.445218719, -5.445218719}
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