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Simplifying 14x2 = 2x + 11 Reorder the terms: 14x2 = 11 + 2x Solving 14x2 = 11 + 2x Solving for variable 'x'. Reorder the terms: -11 + -2x + 14x2 = 11 + 2x + -11 + -2x Reorder the terms: -11 + -2x + 14x2 = 11 + -11 + 2x + -2x Combine like terms: 11 + -11 = 0 -11 + -2x + 14x2 = 0 + 2x + -2x -11 + -2x + 14x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -11 + -2x + 14x2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -0.7857142857 + -0.1428571429x + x2 = 0 Move the constant term to the right: Add '0.7857142857' to each side of the equation. -0.7857142857 + -0.1428571429x + 0.7857142857 + x2 = 0 + 0.7857142857 Reorder the terms: -0.7857142857 + 0.7857142857 + -0.1428571429x + x2 = 0 + 0.7857142857 Combine like terms: -0.7857142857 + 0.7857142857 = 0.0000000000 0.0000000000 + -0.1428571429x + x2 = 0 + 0.7857142857 -0.1428571429x + x2 = 0 + 0.7857142857 Combine like terms: 0 + 0.7857142857 = 0.7857142857 -0.1428571429x + x2 = 0.7857142857 The x term is -0.1428571429x. Take half its coefficient (-0.07142857145). Square it (0.005102040819) and add it to both sides. Add '0.005102040819' to each side of the equation. -0.1428571429x + 0.005102040819 + x2 = 0.7857142857 + 0.005102040819 Reorder the terms: 0.005102040819 + -0.1428571429x + x2 = 0.7857142857 + 0.005102040819 Combine like terms: 0.7857142857 + 0.005102040819 = 0.790816326519 0.005102040819 + -0.1428571429x + x2 = 0.790816326519 Factor a perfect square on the left side: (x + -0.07142857145)(x + -0.07142857145) = 0.790816326519 Calculate the square root of the right side: 0.889278543 Break this problem into two subproblems by setting (x + -0.07142857145) equal to 0.889278543 and -0.889278543.Subproblem 1
x + -0.07142857145 = 0.889278543 Simplifying x + -0.07142857145 = 0.889278543 Reorder the terms: -0.07142857145 + x = 0.889278543 Solving -0.07142857145 + x = 0.889278543 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.07142857145' to each side of the equation. -0.07142857145 + 0.07142857145 + x = 0.889278543 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + x = 0.889278543 + 0.07142857145 x = 0.889278543 + 0.07142857145 Combine like terms: 0.889278543 + 0.07142857145 = 0.96070711445 x = 0.96070711445 Simplifying x = 0.96070711445Subproblem 2
x + -0.07142857145 = -0.889278543 Simplifying x + -0.07142857145 = -0.889278543 Reorder the terms: -0.07142857145 + x = -0.889278543 Solving -0.07142857145 + x = -0.889278543 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.07142857145' to each side of the equation. -0.07142857145 + 0.07142857145 + x = -0.889278543 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + x = -0.889278543 + 0.07142857145 x = -0.889278543 + 0.07142857145 Combine like terms: -0.889278543 + 0.07142857145 = -0.81784997155 x = -0.81784997155 Simplifying x = -0.81784997155Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.96070711445, -0.81784997155}
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