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Simplifying x2 + -24x + 99 = 0 Reorder the terms: 99 + -24x + x2 = 0 Solving 99 + -24x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-99' to each side of the equation. 99 + -24x + -99 + x2 = 0 + -99 Reorder the terms: 99 + -99 + -24x + x2 = 0 + -99 Combine like terms: 99 + -99 = 0 0 + -24x + x2 = 0 + -99 -24x + x2 = 0 + -99 Combine like terms: 0 + -99 = -99 -24x + x2 = -99 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 = -99 + 144 Reorder the terms: 144 + -24x + x2 = -99 + 144 Combine like terms: -99 + 144 = 45 144 + -24x + x2 = 45 Factor a perfect square on the left side: (x + -12)(x + -12) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (x + -12) equal to 6.708203933 and -6.708203933.Subproblem 1
x + -12 = 6.708203933 Simplifying x + -12 = 6.708203933 Reorder the terms: -12 + x = 6.708203933 Solving -12 + x = 6.708203933 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 = 6.708203933 + 12 Combine like terms: -12 + 12 = 0 0 + x = 6.708203933 + 12 x = 6.708203933 + 12 Combine like terms: 6.708203933 + 12 = 18.708203933 x = 18.708203933 Simplifying x = 18.708203933Subproblem 2
x + -12 = -6.708203933 Simplifying x + -12 = -6.708203933 Reorder the terms: -12 + x = -6.708203933 Solving -12 + x = -6.708203933 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 = -6.708203933 + 12 Combine like terms: -12 + 12 = 0 0 + x = -6.708203933 + 12 x = -6.708203933 + 12 Combine like terms: -6.708203933 + 12 = 5.291796067 x = 5.291796067 Simplifying x = 5.291796067Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.708203933, 5.291796067}
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