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Simplifying 133x + -1x2 = 1 Solving 133x + -1x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + 133x + -1x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + 133x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 1 + -133x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -133x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -133x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -133x + x2 = 0 + -1 -133x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -133x + x2 = -1 The x term is -133x. Take half its coefficient (-66.5). Square it (4422.25) and add it to both sides. Add '4422.25' to each side of the equation. -133x + 4422.25 + x2 = -1 + 4422.25 Reorder the terms: 4422.25 + -133x + x2 = -1 + 4422.25 Combine like terms: -1 + 4422.25 = 4421.25 4422.25 + -133x + x2 = 4421.25 Factor a perfect square on the left side: (x + -66.5)(x + -66.5) = 4421.25 Calculate the square root of the right side: 66.492480778 Break this problem into two subproblems by setting (x + -66.5) equal to 66.492480778 and -66.492480778.Subproblem 1
x + -66.5 = 66.492480778 Simplifying x + -66.5 = 66.492480778 Reorder the terms: -66.5 + x = 66.492480778 Solving -66.5 + x = 66.492480778 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '66.5' to each side of the equation. -66.5 + 66.5 + x = 66.492480778 + 66.5 Combine like terms: -66.5 + 66.5 = 0.0 0.0 + x = 66.492480778 + 66.5 x = 66.492480778 + 66.5 Combine like terms: 66.492480778 + 66.5 = 132.992480778 x = 132.992480778 Simplifying x = 132.992480778Subproblem 2
x + -66.5 = -66.492480778 Simplifying x + -66.5 = -66.492480778 Reorder the terms: -66.5 + x = -66.492480778 Solving -66.5 + x = -66.492480778 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '66.5' to each side of the equation. -66.5 + 66.5 + x = -66.492480778 + 66.5 Combine like terms: -66.5 + 66.5 = 0.0 0.0 + x = -66.492480778 + 66.5 x = -66.492480778 + 66.5 Combine like terms: -66.492480778 + 66.5 = 0.007519222 x = 0.007519222 Simplifying x = 0.007519222Solution
The solution to the problem is based on the solutions from the subproblems. x = {132.992480778, 0.007519222}
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