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Simplifying -1x2 + 7x = 1 Reorder the terms: 7x + -1x2 = 1 Solving 7x + -1x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + 7x + -1x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + 7x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 1 + -7x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -7x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -7x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -7x + x2 = 0 + -1 -7x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -7x + x2 = -1 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = -1 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -1 + 12.25 Combine like terms: -1 + 12.25 = 11.25 12.25 + -7x + x2 = 11.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 11.25 Calculate the square root of the right side: 3.354101966 Break this problem into two subproblems by setting (x + -3.5) equal to 3.354101966 and -3.354101966.Subproblem 1
x + -3.5 = 3.354101966 Simplifying x + -3.5 = 3.354101966 Reorder the terms: -3.5 + x = 3.354101966 Solving -3.5 + x = 3.354101966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 3.354101966 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 3.354101966 + 3.5 x = 3.354101966 + 3.5 Combine like terms: 3.354101966 + 3.5 = 6.854101966 x = 6.854101966 Simplifying x = 6.854101966Subproblem 2
x + -3.5 = -3.354101966 Simplifying x + -3.5 = -3.354101966 Reorder the terms: -3.5 + x = -3.354101966 Solving -3.5 + x = -3.354101966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -3.354101966 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -3.354101966 + 3.5 x = -3.354101966 + 3.5 Combine like terms: -3.354101966 + 3.5 = 0.145898034 x = 0.145898034 Simplifying x = 0.145898034Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.854101966, 0.145898034}
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