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Simplifying x2 + 8 + -24x = 0 Reorder the terms: 8 + -24x + x2 = 0 Solving 8 + -24x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + -24x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + -24x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -24x + x2 = 0 + -8 -24x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 -24x + x2 = -8 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 = -8 + 144 Reorder the terms: 144 + -24x + x2 = -8 + 144 Combine like terms: -8 + 144 = 136 144 + -24x + x2 = 136 Factor a perfect square on the left side: (x + -12)(x + -12) = 136 Calculate the square root of the right side: 11.66190379 Break this problem into two subproblems by setting (x + -12) equal to 11.66190379 and -11.66190379.Subproblem 1
x + -12 = 11.66190379 Simplifying x + -12 = 11.66190379 Reorder the terms: -12 + x = 11.66190379 Solving -12 + x = 11.66190379 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 = 11.66190379 + 12 Combine like terms: -12 + 12 = 0 0 + x = 11.66190379 + 12 x = 11.66190379 + 12 Combine like terms: 11.66190379 + 12 = 23.66190379 x = 23.66190379 Simplifying x = 23.66190379Subproblem 2
x + -12 = -11.66190379 Simplifying x + -12 = -11.66190379 Reorder the terms: -12 + x = -11.66190379 Solving -12 + x = -11.66190379 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 = -11.66190379 + 12 Combine like terms: -12 + 12 = 0 0 + x = -11.66190379 + 12 x = -11.66190379 + 12 Combine like terms: -11.66190379 + 12 = 0.33809621 x = 0.33809621 Simplifying x = 0.33809621Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.66190379, 0.33809621}
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