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Simplifying 0 = 7x2 + 7x + -1 Reorder the terms: 0 = -1 + 7x + 7x2 Solving 0 = -1 + 7x + 7x2 Solving for variable 'x'. Combine like terms: 0 + 1 = 1 1 + -7x + -7x2 = -1 + 7x + 7x2 + 1 + -7x + -7x2 Reorder the terms: 1 + -7x + -7x2 = -1 + 1 + 7x + -7x + 7x2 + -7x2 Combine like terms: -1 + 1 = 0 1 + -7x + -7x2 = 0 + 7x + -7x + 7x2 + -7x2 1 + -7x + -7x2 = 7x + -7x + 7x2 + -7x2 Combine like terms: 7x + -7x = 0 1 + -7x + -7x2 = 0 + 7x2 + -7x2 1 + -7x + -7x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 1 + -7x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -0.1428571429 + x + x2 = 0 Move the constant term to the right: Add '0.1428571429' to each side of the equation. -0.1428571429 + x + 0.1428571429 + x2 = 0 + 0.1428571429 Reorder the terms: -0.1428571429 + 0.1428571429 + x + x2 = 0 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x + x2 = 0 + 0.1428571429 x + x2 = 0 + 0.1428571429 Combine like terms: 0 + 0.1428571429 = 0.1428571429 x + x2 = 0.1428571429 The x term is x. 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. + 0.25 + x2 = 0.1428571429 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 0.1428571429 + 0.25 Combine like terms: 0.1428571429 + 0.25 = 0.3928571429 1.25 + 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 = 0.126783171 x = 0.126783171 Simplifying x = 0.126783171Subproblem 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 = -1.126783171 x = -1.126783171 Simplifying x = -1.126783171Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.126783171, -1.126783171}
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