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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 = 162 144 + -24x + x2 = 162 Factor a perfect square on the left side: (x + -12)(x + -12) = 162 Calculate the square root of the right side: 12.727922061 Break this problem into two subproblems by setting (x + -12) equal to 12.727922061 and -12.727922061.Subproblem 1
x + -12 = 12.727922061 Simplifying x + -12 = 12.727922061 Reorder the terms: -12 + x = 12.727922061 Solving -12 + x = 12.727922061 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 = 12.727922061 + 12 Combine like terms: -12 + 12 = 0 0 + x = 12.727922061 + 12 x = 12.727922061 + 12 Combine like terms: 12.727922061 + 12 = 24.727922061 x = 24.727922061 Simplifying x = 24.727922061Subproblem 2
x + -12 = -12.727922061 Simplifying x + -12 = -12.727922061 Reorder the terms: -12 + x = -12.727922061 Solving -12 + x = -12.727922061 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 = -12.727922061 + 12 Combine like terms: -12 + 12 = 0 0 + x = -12.727922061 + 12 x = -12.727922061 + 12 Combine like terms: -12.727922061 + 12 = -0.727922061 x = -0.727922061 Simplifying x = -0.727922061Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.727922061, -0.727922061}
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