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Simplifying 11x2 + 14x + -1 = 0 Reorder the terms: -1 + 14x + 11x2 = 0 Solving -1 + 14x + 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'. -0.09090909091 + 1.272727273x + x2 = 0 Move the constant term to the right: Add '0.09090909091' to each side of the equation. -0.09090909091 + 1.272727273x + 0.09090909091 + x2 = 0 + 0.09090909091 Reorder the terms: -0.09090909091 + 0.09090909091 + 1.272727273x + x2 = 0 + 0.09090909091 Combine like terms: -0.09090909091 + 0.09090909091 = 0.00000000000 0.00000000000 + 1.272727273x + x2 = 0 + 0.09090909091 1.272727273x + x2 = 0 + 0.09090909091 Combine like terms: 0 + 0.09090909091 = 0.09090909091 1.272727273x + x2 = 0.09090909091 The x term is 1.272727273x. Take half its coefficient (0.6363636365). Square it (0.4049586779) and add it to both sides. Add '0.4049586779' to each side of the equation. 1.272727273x + 0.4049586779 + x2 = 0.09090909091 + 0.4049586779 Reorder the terms: 0.4049586779 + 1.272727273x + x2 = 0.09090909091 + 0.4049586779 Combine like terms: 0.09090909091 + 0.4049586779 = 0.49586776881 0.4049586779 + 1.272727273x + x2 = 0.49586776881 Factor a perfect square on the left side: (x + 0.6363636365)(x + 0.6363636365) = 0.49586776881 Calculate the square root of the right side: 0.70417879 Break this problem into two subproblems by setting (x + 0.6363636365) equal to 0.70417879 and -0.70417879.Subproblem 1
x + 0.6363636365 = 0.70417879 Simplifying x + 0.6363636365 = 0.70417879 Reorder the terms: 0.6363636365 + x = 0.70417879 Solving 0.6363636365 + x = 0.70417879 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6363636365' to each side of the equation. 0.6363636365 + -0.6363636365 + x = 0.70417879 + -0.6363636365 Combine like terms: 0.6363636365 + -0.6363636365 = 0.0000000000 0.0000000000 + x = 0.70417879 + -0.6363636365 x = 0.70417879 + -0.6363636365 Combine like terms: 0.70417879 + -0.6363636365 = 0.0678151535 x = 0.0678151535 Simplifying x = 0.0678151535Subproblem 2
x + 0.6363636365 = -0.70417879 Simplifying x + 0.6363636365 = -0.70417879 Reorder the terms: 0.6363636365 + x = -0.70417879 Solving 0.6363636365 + x = -0.70417879 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6363636365' to each side of the equation. 0.6363636365 + -0.6363636365 + x = -0.70417879 + -0.6363636365 Combine like terms: 0.6363636365 + -0.6363636365 = 0.0000000000 0.0000000000 + x = -0.70417879 + -0.6363636365 x = -0.70417879 + -0.6363636365 Combine like terms: -0.70417879 + -0.6363636365 = -1.3405424265 x = -1.3405424265 Simplifying x = -1.3405424265Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.0678151535, -1.3405424265}
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