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Simplifying 6 + -7(x + -1) * x = 7 Reorder the terms: 6 + -7(-1 + x) * x = 7 Reorder the terms for easier multiplication: 6 + -7x(-1 + x) = 7 6 + (-1 * -7x + x * -7x) = 7 6 + (7x + -7x2) = 7 Solving 6 + 7x + -7x2 = 7 Solving for variable 'x'. Reorder the terms: 6 + -7 + 7x + -7x2 = 7 + -7 Combine like terms: 6 + -7 = -1 -1 + 7x + -7x2 = 7 + -7 Combine like terms: 7 + -7 = 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 + -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 = 0.1071428571 0.25 + -1x + x2 = 0.1071428571 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.1071428571 Calculate the square root of the right side: 0.327326835 Break this problem into two subproblems by setting (x + -0.5) equal to 0.327326835 and -0.327326835.Subproblem 1
x + -0.5 = 0.327326835 Simplifying x + -0.5 = 0.327326835 Reorder the terms: -0.5 + x = 0.327326835 Solving -0.5 + x = 0.327326835 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 = 0.327326835 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.327326835 + 0.5 x = 0.327326835 + 0.5 Combine like terms: 0.327326835 + 0.5 = 0.827326835 x = 0.827326835 Simplifying x = 0.827326835Subproblem 2
x + -0.5 = -0.327326835 Simplifying x + -0.5 = -0.327326835 Reorder the terms: -0.5 + x = -0.327326835 Solving -0.5 + x = -0.327326835 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 = -0.327326835 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.327326835 + 0.5 x = -0.327326835 + 0.5 Combine like terms: -0.327326835 + 0.5 = 0.172673165 x = 0.172673165 Simplifying x = 0.172673165Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.827326835, 0.172673165}
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