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Simplifying x2 + -24x + -224 = 0 Reorder the terms: -224 + -24x + x2 = 0 Solving -224 + -24x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '224' to each side of the equation. -224 + -24x + 224 + x2 = 0 + 224 Reorder the terms: -224 + 224 + -24x + x2 = 0 + 224 Combine like terms: -224 + 224 = 0 0 + -24x + x2 = 0 + 224 -24x + x2 = 0 + 224 Combine like terms: 0 + 224 = 224 -24x + x2 = 224 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 = 224 + 144 Reorder the terms: 144 + -24x + x2 = 224 + 144 Combine like terms: 224 + 144 = 368 144 + -24x + x2 = 368 Factor a perfect square on the left side: (x + -12)(x + -12) = 368 Calculate the square root of the right side: 19.183326093 Break this problem into two subproblems by setting (x + -12) equal to 19.183326093 and -19.183326093.Subproblem 1
x + -12 = 19.183326093 Simplifying x + -12 = 19.183326093 Reorder the terms: -12 + x = 19.183326093 Solving -12 + x = 19.183326093 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 = 19.183326093 + 12 Combine like terms: -12 + 12 = 0 0 + x = 19.183326093 + 12 x = 19.183326093 + 12 Combine like terms: 19.183326093 + 12 = 31.183326093 x = 31.183326093 Simplifying x = 31.183326093Subproblem 2
x + -12 = -19.183326093 Simplifying x + -12 = -19.183326093 Reorder the terms: -12 + x = -19.183326093 Solving -12 + x = -19.183326093 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 = -19.183326093 + 12 Combine like terms: -12 + 12 = 0 0 + x = -19.183326093 + 12 x = -19.183326093 + 12 Combine like terms: -19.183326093 + 12 = -7.183326093 x = -7.183326093 Simplifying x = -7.183326093Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.183326093, -7.183326093}
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