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Simplifying x2 + -2x + -13824 = 0 Reorder the terms: -13824 + -2x + x2 = 0 Solving -13824 + -2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '13824' to each side of the equation. -13824 + -2x + 13824 + x2 = 0 + 13824 Reorder the terms: -13824 + 13824 + -2x + x2 = 0 + 13824 Combine like terms: -13824 + 13824 = 0 0 + -2x + x2 = 0 + 13824 -2x + x2 = 0 + 13824 Combine like terms: 0 + 13824 = 13824 -2x + x2 = 13824 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 13824 + 1 Reorder the terms: 1 + -2x + x2 = 13824 + 1 Combine like terms: 13824 + 1 = 13825 1 + -2x + x2 = 13825 Factor a perfect square on the left side: (x + -1)(x + -1) = 13825 Calculate the square root of the right side: 117.579760163 Break this problem into two subproblems by setting (x + -1) equal to 117.579760163 and -117.579760163.Subproblem 1
x + -1 = 117.579760163 Simplifying x + -1 = 117.579760163 Reorder the terms: -1 + x = 117.579760163 Solving -1 + x = 117.579760163 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 117.579760163 + 1 Combine like terms: -1 + 1 = 0 0 + x = 117.579760163 + 1 x = 117.579760163 + 1 Combine like terms: 117.579760163 + 1 = 118.579760163 x = 118.579760163 Simplifying x = 118.579760163Subproblem 2
x + -1 = -117.579760163 Simplifying x + -1 = -117.579760163 Reorder the terms: -1 + x = -117.579760163 Solving -1 + x = -117.579760163 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -117.579760163 + 1 Combine like terms: -1 + 1 = 0 0 + x = -117.579760163 + 1 x = -117.579760163 + 1 Combine like terms: -117.579760163 + 1 = -116.579760163 x = -116.579760163 Simplifying x = -116.579760163Solution
The solution to the problem is based on the solutions from the subproblems. x = {118.579760163, -116.579760163}
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