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Simplifying 6x + 1 = x2 + -1x Reorder the terms: 1 + 6x = x2 + -1x Reorder the terms: 1 + 6x = -1x + x2 Solving 1 + 6x = -1x + x2 Solving for variable 'x'. Combine like terms: 6x + x = 7x 1 + 7x + -1x2 = -1x + x2 + x + -1x2 Reorder the terms: 1 + 7x + -1x2 = -1x + x + x2 + -1x2 Combine like terms: -1x + x = 0 1 + 7x + -1x2 = 0 + x2 + -1x2 1 + 7x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 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 = 13.25 12.25 + -7x + x2 = 13.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 13.25 Calculate the square root of the right side: 3.640054945 Break this problem into two subproblems by setting (x + -3.5) equal to 3.640054945 and -3.640054945.Subproblem 1
x + -3.5 = 3.640054945 Simplifying x + -3.5 = 3.640054945 Reorder the terms: -3.5 + x = 3.640054945 Solving -3.5 + x = 3.640054945 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 = 3.640054945 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 3.640054945 + 3.5 x = 3.640054945 + 3.5 Combine like terms: 3.640054945 + 3.5 = 7.140054945 x = 7.140054945 Simplifying x = 7.140054945Subproblem 2
x + -3.5 = -3.640054945 Simplifying x + -3.5 = -3.640054945 Reorder the terms: -3.5 + x = -3.640054945 Solving -3.5 + x = -3.640054945 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 = -3.640054945 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -3.640054945 + 3.5 x = -3.640054945 + 3.5 Combine like terms: -3.640054945 + 3.5 = -0.140054945 x = -0.140054945 Simplifying x = -0.140054945Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.140054945, -0.140054945}
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