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Simplifying 140 = x2 + 2x + 12 Reorder the terms: 140 = 12 + 2x + x2 Solving 140 = 12 + 2x + x2 Solving for variable 'x'. Combine like terms: 140 + -12 = 128 128 + -2x + -1x2 = 12 + 2x + x2 + -12 + -2x + -1x2 Reorder the terms: 128 + -2x + -1x2 = 12 + -12 + 2x + -2x + x2 + -1x2 Combine like terms: 12 + -12 = 0 128 + -2x + -1x2 = 0 + 2x + -2x + x2 + -1x2 128 + -2x + -1x2 = 2x + -2x + x2 + -1x2 Combine like terms: 2x + -2x = 0 128 + -2x + -1x2 = 0 + x2 + -1x2 128 + -2x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 128 + -2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -128 + 2x + x2 = 0 Move the constant term to the right: Add '128' to each side of the equation. -128 + 2x + 128 + x2 = 0 + 128 Reorder the terms: -128 + 128 + 2x + x2 = 0 + 128 Combine like terms: -128 + 128 = 0 0 + 2x + x2 = 0 + 128 2x + x2 = 0 + 128 Combine like terms: 0 + 128 = 128 2x + x2 = 128 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 = 128 + 1 Reorder the terms: 1 + 2x + x2 = 128 + 1 Combine like terms: 128 + 1 = 129 1 + 2x + x2 = 129 Factor a perfect square on the left side: (x + 1)(x + 1) = 129 Calculate the square root of the right side: 11.357816692 Break this problem into two subproblems by setting (x + 1) equal to 11.357816692 and -11.357816692.Subproblem 1
x + 1 = 11.357816692 Simplifying x + 1 = 11.357816692 Reorder the terms: 1 + x = 11.357816692 Solving 1 + x = 11.357816692 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 = 11.357816692 + -1 Combine like terms: 1 + -1 = 0 0 + x = 11.357816692 + -1 x = 11.357816692 + -1 Combine like terms: 11.357816692 + -1 = 10.357816692 x = 10.357816692 Simplifying x = 10.357816692Subproblem 2
x + 1 = -11.357816692 Simplifying x + 1 = -11.357816692 Reorder the terms: 1 + x = -11.357816692 Solving 1 + x = -11.357816692 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 = -11.357816692 + -1 Combine like terms: 1 + -1 = 0 0 + x = -11.357816692 + -1 x = -11.357816692 + -1 Combine like terms: -11.357816692 + -1 = -12.357816692 x = -12.357816692 Simplifying x = -12.357816692Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.357816692, -12.357816692}
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