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Simplifying x2 + -24x + -2000 = 0 Reorder the terms: -2000 + -24x + x2 = 0 Solving -2000 + -24x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2000' to each side of the equation. -2000 + -24x + 2000 + x2 = 0 + 2000 Reorder the terms: -2000 + 2000 + -24x + x2 = 0 + 2000 Combine like terms: -2000 + 2000 = 0 0 + -24x + x2 = 0 + 2000 -24x + x2 = 0 + 2000 Combine like terms: 0 + 2000 = 2000 -24x + x2 = 2000 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 = 2000 + 144 Reorder the terms: 144 + -24x + x2 = 2000 + 144 Combine like terms: 2000 + 144 = 2144 144 + -24x + x2 = 2144 Factor a perfect square on the left side: (x + -12)(x + -12) = 2144 Calculate the square root of the right side: 46.303347611 Break this problem into two subproblems by setting (x + -12) equal to 46.303347611 and -46.303347611.Subproblem 1
x + -12 = 46.303347611 Simplifying x + -12 = 46.303347611 Reorder the terms: -12 + x = 46.303347611 Solving -12 + x = 46.303347611 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 = 46.303347611 + 12 Combine like terms: -12 + 12 = 0 0 + x = 46.303347611 + 12 x = 46.303347611 + 12 Combine like terms: 46.303347611 + 12 = 58.303347611 x = 58.303347611 Simplifying x = 58.303347611Subproblem 2
x + -12 = -46.303347611 Simplifying x + -12 = -46.303347611 Reorder the terms: -12 + x = -46.303347611 Solving -12 + x = -46.303347611 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 = -46.303347611 + 12 Combine like terms: -12 + 12 = 0 0 + x = -46.303347611 + 12 x = -46.303347611 + 12 Combine like terms: -46.303347611 + 12 = -34.303347611 x = -34.303347611 Simplifying x = -34.303347611Solution
The solution to the problem is based on the solutions from the subproblems. x = {58.303347611, -34.303347611}
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