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Simplifying -7x2 + -11x + -1 = 0 Reorder the terms: -1 + -11x + -7x2 = 0 Solving -1 + -11x + -7x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(1 + 11x + 7x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(1 + 11x + 7x2)' equal to zero and attempt to solve: Simplifying 1 + 11x + 7x2 = 0 Solving 1 + 11x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.1428571429 + 1.571428571x + x2 = 0 Move the constant term to the right: Add '-0.1428571429' to each side of the equation. 0.1428571429 + 1.571428571x + -0.1428571429 + x2 = 0 + -0.1428571429 Reorder the terms: 0.1428571429 + -0.1428571429 + 1.571428571x + x2 = 0 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + 1.571428571x + x2 = 0 + -0.1428571429 1.571428571x + x2 = 0 + -0.1428571429 Combine like terms: 0 + -0.1428571429 = -0.1428571429 1.571428571x + x2 = -0.1428571429 The x term is 1.571428571x. Take half its coefficient (0.7857142855). Square it (0.6173469384) and add it to both sides. Add '0.6173469384' to each side of the equation. 1.571428571x + 0.6173469384 + x2 = -0.1428571429 + 0.6173469384 Reorder the terms: 0.6173469384 + 1.571428571x + x2 = -0.1428571429 + 0.6173469384 Combine like terms: -0.1428571429 + 0.6173469384 = 0.4744897955 0.6173469384 + 1.571428571x + x2 = 0.4744897955 Factor a perfect square on the left side: (x + 0.7857142855)(x + 0.7857142855) = 0.4744897955 Calculate the square root of the right side: 0.688832197 Break this problem into two subproblems by setting (x + 0.7857142855) equal to 0.688832197 and -0.688832197.Subproblem 1
x + 0.7857142855 = 0.688832197 Simplifying x + 0.7857142855 = 0.688832197 Reorder the terms: 0.7857142855 + x = 0.688832197 Solving 0.7857142855 + x = 0.688832197 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7857142855' to each side of the equation. 0.7857142855 + -0.7857142855 + x = 0.688832197 + -0.7857142855 Combine like terms: 0.7857142855 + -0.7857142855 = 0.0000000000 0.0000000000 + x = 0.688832197 + -0.7857142855 x = 0.688832197 + -0.7857142855 Combine like terms: 0.688832197 + -0.7857142855 = -0.0968820885 x = -0.0968820885 Simplifying x = -0.0968820885Subproblem 2
x + 0.7857142855 = -0.688832197 Simplifying x + 0.7857142855 = -0.688832197 Reorder the terms: 0.7857142855 + x = -0.688832197 Solving 0.7857142855 + x = -0.688832197 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7857142855' to each side of the equation. 0.7857142855 + -0.7857142855 + x = -0.688832197 + -0.7857142855 Combine like terms: 0.7857142855 + -0.7857142855 = 0.0000000000 0.0000000000 + x = -0.688832197 + -0.7857142855 x = -0.688832197 + -0.7857142855 Combine like terms: -0.688832197 + -0.7857142855 = -1.4745464825 x = -1.4745464825 Simplifying x = -1.4745464825Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.0968820885, -1.4745464825}Solution
x = {-0.0968820885, -1.4745464825}
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