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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 = 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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