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Simplifying 169 = x2 + -2x + 37 Reorder the terms: 169 = 37 + -2x + x2 Solving 169 = 37 + -2x + x2 Solving for variable 'x'. Combine like terms: 169 + -37 = 132 132 + 2x + -1x2 = 37 + -2x + x2 + -37 + 2x + -1x2 Reorder the terms: 132 + 2x + -1x2 = 37 + -37 + -2x + 2x + x2 + -1x2 Combine like terms: 37 + -37 = 0 132 + 2x + -1x2 = 0 + -2x + 2x + x2 + -1x2 132 + 2x + -1x2 = -2x + 2x + x2 + -1x2 Combine like terms: -2x + 2x = 0 132 + 2x + -1x2 = 0 + x2 + -1x2 132 + 2x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 132 + 2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -132 + -2x + x2 = 0 Move the constant term to the right: Add '132' to each side of the equation. -132 + -2x + 132 + x2 = 0 + 132 Reorder the terms: -132 + 132 + -2x + x2 = 0 + 132 Combine like terms: -132 + 132 = 0 0 + -2x + x2 = 0 + 132 -2x + x2 = 0 + 132 Combine like terms: 0 + 132 = 132 -2x + x2 = 132 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 = 132 + 1 Reorder the terms: 1 + -2x + x2 = 132 + 1 Combine like terms: 132 + 1 = 133 1 + -2x + x2 = 133 Factor a perfect square on the left side: (x + -1)(x + -1) = 133 Calculate the square root of the right side: 11.532562595 Break this problem into two subproblems by setting (x + -1) equal to 11.532562595 and -11.532562595.Subproblem 1
x + -1 = 11.532562595 Simplifying x + -1 = 11.532562595 Reorder the terms: -1 + x = 11.532562595 Solving -1 + x = 11.532562595 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 = 11.532562595 + 1 Combine like terms: -1 + 1 = 0 0 + x = 11.532562595 + 1 x = 11.532562595 + 1 Combine like terms: 11.532562595 + 1 = 12.532562595 x = 12.532562595 Simplifying x = 12.532562595Subproblem 2
x + -1 = -11.532562595 Simplifying x + -1 = -11.532562595 Reorder the terms: -1 + x = -11.532562595 Solving -1 + x = -11.532562595 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 = -11.532562595 + 1 Combine like terms: -1 + 1 = 0 0 + x = -11.532562595 + 1 x = -11.532562595 + 1 Combine like terms: -11.532562595 + 1 = -10.532562595 x = -10.532562595 Simplifying x = -10.532562595Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.532562595, -10.532562595}
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