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Simplifying x2 + -26x + -144 = 0 Reorder the terms: -144 + -26x + x2 = 0 Solving -144 + -26x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '144' to each side of the equation. -144 + -26x + 144 + x2 = 0 + 144 Reorder the terms: -144 + 144 + -26x + x2 = 0 + 144 Combine like terms: -144 + 144 = 0 0 + -26x + x2 = 0 + 144 -26x + x2 = 0 + 144 Combine like terms: 0 + 144 = 144 -26x + x2 = 144 The x term is -26x. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26x + 169 + x2 = 144 + 169 Reorder the terms: 169 + -26x + x2 = 144 + 169 Combine like terms: 144 + 169 = 313 169 + -26x + x2 = 313 Factor a perfect square on the left side: (x + -13)(x + -13) = 313 Calculate the square root of the right side: 17.691806013 Break this problem into two subproblems by setting (x + -13) equal to 17.691806013 and -17.691806013.Subproblem 1
x + -13 = 17.691806013 Simplifying x + -13 = 17.691806013 Reorder the terms: -13 + x = 17.691806013 Solving -13 + x = 17.691806013 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = 17.691806013 + 13 Combine like terms: -13 + 13 = 0 0 + x = 17.691806013 + 13 x = 17.691806013 + 13 Combine like terms: 17.691806013 + 13 = 30.691806013 x = 30.691806013 Simplifying x = 30.691806013Subproblem 2
x + -13 = -17.691806013 Simplifying x + -13 = -17.691806013 Reorder the terms: -13 + x = -17.691806013 Solving -13 + x = -17.691806013 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = -17.691806013 + 13 Combine like terms: -13 + 13 = 0 0 + x = -17.691806013 + 13 x = -17.691806013 + 13 Combine like terms: -17.691806013 + 13 = -4.691806013 x = -4.691806013 Simplifying x = -4.691806013Solution
The solution to the problem is based on the solutions from the subproblems. x = {30.691806013, -4.691806013}
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