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Simplifying 7x2 + -7x + -1 = 0 Reorder the terms: -1 + -7x + 7x2 = 0 Solving -1 + -7x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.1428571429 + -1x + x2 = 0 Move the constant term to the right: Add '0.1428571429' to each side of the equation. -0.1428571429 + -1x + 0.1428571429 + x2 = 0 + 0.1428571429 Reorder the terms: -0.1428571429 + 0.1428571429 + -1x + x2 = 0 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + -1x + x2 = 0 + 0.1428571429 -1x + x2 = 0 + 0.1428571429 Combine like terms: 0 + 0.1428571429 = 0.1428571429 -1x + x2 = 0.1428571429 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 0.1428571429 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 0.1428571429 + 0.25 Combine like terms: 0.1428571429 + 0.25 = 0.3928571429 0.25 + -1x + x2 = 0.3928571429 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.3928571429 Calculate the square root of the right side: 0.626783171 Break this problem into two subproblems by setting (x + -0.5) equal to 0.626783171 and -0.626783171.Subproblem 1
x + -0.5 = 0.626783171 Simplifying x + -0.5 = 0.626783171 Reorder the terms: -0.5 + x = 0.626783171 Solving -0.5 + x = 0.626783171 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 0.626783171 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.626783171 + 0.5 x = 0.626783171 + 0.5 Combine like terms: 0.626783171 + 0.5 = 1.126783171 x = 1.126783171 Simplifying x = 1.126783171Subproblem 2
x + -0.5 = -0.626783171 Simplifying x + -0.5 = -0.626783171 Reorder the terms: -0.5 + x = -0.626783171 Solving -0.5 + x = -0.626783171 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -0.626783171 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.626783171 + 0.5 x = -0.626783171 + 0.5 Combine like terms: -0.626783171 + 0.5 = -0.126783171 x = -0.126783171 Simplifying x = -0.126783171Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.126783171, -0.126783171}
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