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Simplifying 0 = x2 + -24x + -140 Reorder the terms: 0 = -140 + -24x + x2 Solving 0 = -140 + -24x + x2 Solving for variable 'x'. Combine like terms: 0 + 140 = 140 140 + 24x + -1x2 = -140 + -24x + x2 + 140 + 24x + -1x2 Reorder the terms: 140 + 24x + -1x2 = -140 + 140 + -24x + 24x + x2 + -1x2 Combine like terms: -140 + 140 = 0 140 + 24x + -1x2 = 0 + -24x + 24x + x2 + -1x2 140 + 24x + -1x2 = -24x + 24x + x2 + -1x2 Combine like terms: -24x + 24x = 0 140 + 24x + -1x2 = 0 + x2 + -1x2 140 + 24x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 140 + 24x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -140 + -24x + x2 = 0 Move the constant term to the right: Add '140' to each side of the equation. -140 + -24x + 140 + x2 = 0 + 140 Reorder the terms: -140 + 140 + -24x + x2 = 0 + 140 Combine like terms: -140 + 140 = 0 0 + -24x + x2 = 0 + 140 -24x + x2 = 0 + 140 Combine like terms: 0 + 140 = 140 -24x + x2 = 140 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 = 140 + 144 Reorder the terms: 144 + -24x + x2 = 140 + 144 Combine like terms: 140 + 144 = 284 144 + -24x + x2 = 284 Factor a perfect square on the left side: (x + -12)(x + -12) = 284 Calculate the square root of the right side: 16.852299546 Break this problem into two subproblems by setting (x + -12) equal to 16.852299546 and -16.852299546.Subproblem 1
x + -12 = 16.852299546 Simplifying x + -12 = 16.852299546 Reorder the terms: -12 + x = 16.852299546 Solving -12 + x = 16.852299546 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 = 16.852299546 + 12 Combine like terms: -12 + 12 = 0 0 + x = 16.852299546 + 12 x = 16.852299546 + 12 Combine like terms: 16.852299546 + 12 = 28.852299546 x = 28.852299546 Simplifying x = 28.852299546Subproblem 2
x + -12 = -16.852299546 Simplifying x + -12 = -16.852299546 Reorder the terms: -12 + x = -16.852299546 Solving -12 + x = -16.852299546 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 = -16.852299546 + 12 Combine like terms: -12 + 12 = 0 0 + x = -16.852299546 + 12 x = -16.852299546 + 12 Combine like terms: -16.852299546 + 12 = -4.852299546 x = -4.852299546 Simplifying x = -4.852299546Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.852299546, -4.852299546}
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