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Simplifying x2 + -24x + 18 = 0 Reorder the terms: 18 + -24x + x2 = 0 Solving 18 + -24x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-18' to each side of the equation. 18 + -24x + -18 + x2 = 0 + -18 Reorder the terms: 18 + -18 + -24x + x2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -24x + x2 = 0 + -18 -24x + x2 = 0 + -18 Combine like terms: 0 + -18 = -18 -24x + x2 = -18 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 = -18 + 144 Reorder the terms: 144 + -24x + x2 = -18 + 144 Combine like terms: -18 + 144 = 126 144 + -24x + x2 = 126 Factor a perfect square on the left side: (x + -12)(x + -12) = 126 Calculate the square root of the right side: 11.22497216 Break this problem into two subproblems by setting (x + -12) equal to 11.22497216 and -11.22497216.Subproblem 1
x + -12 = 11.22497216 Simplifying x + -12 = 11.22497216 Reorder the terms: -12 + x = 11.22497216 Solving -12 + x = 11.22497216 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 = 11.22497216 + 12 Combine like terms: -12 + 12 = 0 0 + x = 11.22497216 + 12 x = 11.22497216 + 12 Combine like terms: 11.22497216 + 12 = 23.22497216 x = 23.22497216 Simplifying x = 23.22497216Subproblem 2
x + -12 = -11.22497216 Simplifying x + -12 = -11.22497216 Reorder the terms: -12 + x = -11.22497216 Solving -12 + x = -11.22497216 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 = -11.22497216 + 12 Combine like terms: -12 + 12 = 0 0 + x = -11.22497216 + 12 x = -11.22497216 + 12 Combine like terms: -11.22497216 + 12 = 0.77502784 x = 0.77502784 Simplifying x = 0.77502784Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.22497216, 0.77502784}
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