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Simplifying 0 = x2 + -36x + -124 Reorder the terms: 0 = -124 + -36x + x2 Solving 0 = -124 + -36x + x2 Solving for variable 'x'. Combine like terms: 0 + 124 = 124 124 + 36x + -1x2 = -124 + -36x + x2 + 124 + 36x + -1x2 Reorder the terms: 124 + 36x + -1x2 = -124 + 124 + -36x + 36x + x2 + -1x2 Combine like terms: -124 + 124 = 0 124 + 36x + -1x2 = 0 + -36x + 36x + x2 + -1x2 124 + 36x + -1x2 = -36x + 36x + x2 + -1x2 Combine like terms: -36x + 36x = 0 124 + 36x + -1x2 = 0 + x2 + -1x2 124 + 36x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 124 + 36x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -124 + -36x + x2 = 0 Move the constant term to the right: Add '124' to each side of the equation. -124 + -36x + 124 + x2 = 0 + 124 Reorder the terms: -124 + 124 + -36x + x2 = 0 + 124 Combine like terms: -124 + 124 = 0 0 + -36x + x2 = 0 + 124 -36x + x2 = 0 + 124 Combine like terms: 0 + 124 = 124 -36x + x2 = 124 The x term is -36x. Take half its coefficient (-18). Square it (324) and add it to both sides. Add '324' to each side of the equation. -36x + 324 + x2 = 124 + 324 Reorder the terms: 324 + -36x + x2 = 124 + 324 Combine like terms: 124 + 324 = 448 324 + -36x + x2 = 448 Factor a perfect square on the left side: (x + -18)(x + -18) = 448 Calculate the square root of the right side: 21.166010489 Break this problem into two subproblems by setting (x + -18) equal to 21.166010489 and -21.166010489.Subproblem 1
x + -18 = 21.166010489 Simplifying x + -18 = 21.166010489 Reorder the terms: -18 + x = 21.166010489 Solving -18 + x = 21.166010489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + x = 21.166010489 + 18 Combine like terms: -18 + 18 = 0 0 + x = 21.166010489 + 18 x = 21.166010489 + 18 Combine like terms: 21.166010489 + 18 = 39.166010489 x = 39.166010489 Simplifying x = 39.166010489Subproblem 2
x + -18 = -21.166010489 Simplifying x + -18 = -21.166010489 Reorder the terms: -18 + x = -21.166010489 Solving -18 + x = -21.166010489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + x = -21.166010489 + 18 Combine like terms: -18 + 18 = 0 0 + x = -21.166010489 + 18 x = -21.166010489 + 18 Combine like terms: -21.166010489 + 18 = -3.166010489 x = -3.166010489 Simplifying x = -3.166010489Solution
The solution to the problem is based on the solutions from the subproblems. x = {39.166010489, -3.166010489}
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