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Simplifying 11x2 + 11x + -8 = 0 Reorder the terms: -8 + 11x + 11x2 = 0 Solving -8 + 11x + 11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.7272727273 + x + x2 = 0 Move the constant term to the right: Add '0.7272727273' to each side of the equation. -0.7272727273 + x + 0.7272727273 + x2 = 0 + 0.7272727273 Reorder the terms: -0.7272727273 + 0.7272727273 + x + x2 = 0 + 0.7272727273 Combine like terms: -0.7272727273 + 0.7272727273 = 0.0000000000 0.0000000000 + x + x2 = 0 + 0.7272727273 x + x2 = 0 + 0.7272727273 Combine like terms: 0 + 0.7272727273 = 0.7272727273 x + x2 = 0.7272727273 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 = 0.7272727273 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 0.7272727273 + 0.25 Combine like terms: 0.7272727273 + 0.25 = 0.9772727273 1.25 + x2 = 0.9772727273 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.9772727273 Calculate the square root of the right side: 0.988571053 Break this problem into two subproblems by setting (x + 0.5) equal to 0.988571053 and -0.988571053.Subproblem 1
x + 0.5 = 0.988571053 Simplifying x + 0.5 = 0.988571053 Reorder the terms: 0.5 + x = 0.988571053 Solving 0.5 + x = 0.988571053 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 = 0.988571053 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.988571053 + -0.5 x = 0.988571053 + -0.5 Combine like terms: 0.988571053 + -0.5 = 0.488571053 x = 0.488571053 Simplifying x = 0.488571053Subproblem 2
x + 0.5 = -0.988571053 Simplifying x + 0.5 = -0.988571053 Reorder the terms: 0.5 + x = -0.988571053 Solving 0.5 + x = -0.988571053 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 = -0.988571053 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.988571053 + -0.5 x = -0.988571053 + -0.5 Combine like terms: -0.988571053 + -0.5 = -1.488571053 x = -1.488571053 Simplifying x = -1.488571053Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.488571053, -1.488571053}
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