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Simplifying 14x2 + 11x + -11 = 0 Reorder the terms: -11 + 11x + 14x2 = 0 Solving -11 + 11x + 14x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -0.7857142857 + 0.7857142857x + x2 = 0 Move the constant term to the right: Add '0.7857142857' to each side of the equation. -0.7857142857 + 0.7857142857x + 0.7857142857 + x2 = 0 + 0.7857142857 Reorder the terms: -0.7857142857 + 0.7857142857 + 0.7857142857x + x2 = 0 + 0.7857142857 Combine like terms: -0.7857142857 + 0.7857142857 = 0.0000000000 0.0000000000 + 0.7857142857x + x2 = 0 + 0.7857142857 0.7857142857x + x2 = 0 + 0.7857142857 Combine like terms: 0 + 0.7857142857 = 0.7857142857 0.7857142857x + x2 = 0.7857142857 The x term is 0.7857142857x. Take half its coefficient (0.3928571429). Square it (0.1543367347) and add it to both sides. Add '0.1543367347' to each side of the equation. 0.7857142857x + 0.1543367347 + x2 = 0.7857142857 + 0.1543367347 Reorder the terms: 0.1543367347 + 0.7857142857x + x2 = 0.7857142857 + 0.1543367347 Combine like terms: 0.7857142857 + 0.1543367347 = 0.9400510204 0.1543367347 + 0.7857142857x + x2 = 0.9400510204 Factor a perfect square on the left side: (x + 0.3928571429)(x + 0.3928571429) = 0.9400510204 Calculate the square root of the right side: 0.969562283 Break this problem into two subproblems by setting (x + 0.3928571429) equal to 0.969562283 and -0.969562283.Subproblem 1
x + 0.3928571429 = 0.969562283 Simplifying x + 0.3928571429 = 0.969562283 Reorder the terms: 0.3928571429 + x = 0.969562283 Solving 0.3928571429 + x = 0.969562283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3928571429' to each side of the equation. 0.3928571429 + -0.3928571429 + x = 0.969562283 + -0.3928571429 Combine like terms: 0.3928571429 + -0.3928571429 = 0.0000000000 0.0000000000 + x = 0.969562283 + -0.3928571429 x = 0.969562283 + -0.3928571429 Combine like terms: 0.969562283 + -0.3928571429 = 0.5767051401 x = 0.5767051401 Simplifying x = 0.5767051401Subproblem 2
x + 0.3928571429 = -0.969562283 Simplifying x + 0.3928571429 = -0.969562283 Reorder the terms: 0.3928571429 + x = -0.969562283 Solving 0.3928571429 + x = -0.969562283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3928571429' to each side of the equation. 0.3928571429 + -0.3928571429 + x = -0.969562283 + -0.3928571429 Combine like terms: 0.3928571429 + -0.3928571429 = 0.0000000000 0.0000000000 + x = -0.969562283 + -0.3928571429 x = -0.969562283 + -0.3928571429 Combine like terms: -0.969562283 + -0.3928571429 = -1.3624194259 x = -1.3624194259 Simplifying x = -1.3624194259Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5767051401, -1.3624194259}
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