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Simplifying x2 + -24x + 129 = 0 Reorder the terms: 129 + -24x + x2 = 0 Solving 129 + -24x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-129' to each side of the equation. 129 + -24x + -129 + x2 = 0 + -129 Reorder the terms: 129 + -129 + -24x + x2 = 0 + -129 Combine like terms: 129 + -129 = 0 0 + -24x + x2 = 0 + -129 -24x + x2 = 0 + -129 Combine like terms: 0 + -129 = -129 -24x + x2 = -129 The x term is -24x. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24x + 144 + x2 = -129 + 144 Reorder the terms: 144 + -24x + x2 = -129 + 144 Combine like terms: -129 + 144 = 15 144 + -24x + x2 = 15 Factor a perfect square on the left side: (x + -12)(x + -12) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (x + -12) equal to 3.872983346 and -3.872983346.Subproblem 1
x + -12 = 3.872983346 Simplifying x + -12 = 3.872983346 Reorder the terms: -12 + x = 3.872983346 Solving -12 + x = 3.872983346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 3.872983346 + 12 Combine like terms: -12 + 12 = 0 0 + x = 3.872983346 + 12 x = 3.872983346 + 12 Combine like terms: 3.872983346 + 12 = 15.872983346 x = 15.872983346 Simplifying x = 15.872983346Subproblem 2
x + -12 = -3.872983346 Simplifying x + -12 = -3.872983346 Reorder the terms: -12 + x = -3.872983346 Solving -12 + x = -3.872983346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = -3.872983346 + 12 Combine like terms: -12 + 12 = 0 0 + x = -3.872983346 + 12 x = -3.872983346 + 12 Combine like terms: -3.872983346 + 12 = 8.127016654 x = 8.127016654 Simplifying x = 8.127016654Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.872983346, 8.127016654}
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