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Simplifying 14x2 + 11x + -28 = 0 Reorder the terms: -28 + 11x + 14x2 = 0 Solving -28 + 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'. -2 + 0.7857142857x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 0.7857142857x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 0.7857142857x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 0.7857142857x + x2 = 0 + 2 0.7857142857x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 0.7857142857x + x2 = 2 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 = 2 + 0.1543367347 Reorder the terms: 0.1543367347 + 0.7857142857x + x2 = 2 + 0.1543367347 Combine like terms: 2 + 0.1543367347 = 2.1543367347 0.1543367347 + 0.7857142857x + x2 = 2.1543367347 Factor a perfect square on the left side: (x + 0.3928571429)(x + 0.3928571429) = 2.1543367347 Calculate the square root of the right side: 1.467765899 Break this problem into two subproblems by setting (x + 0.3928571429) equal to 1.467765899 and -1.467765899.Subproblem 1
x + 0.3928571429 = 1.467765899 Simplifying x + 0.3928571429 = 1.467765899 Reorder the terms: 0.3928571429 + x = 1.467765899 Solving 0.3928571429 + x = 1.467765899 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 = 1.467765899 + -0.3928571429 Combine like terms: 0.3928571429 + -0.3928571429 = 0.0000000000 0.0000000000 + x = 1.467765899 + -0.3928571429 x = 1.467765899 + -0.3928571429 Combine like terms: 1.467765899 + -0.3928571429 = 1.0749087561 x = 1.0749087561 Simplifying x = 1.0749087561Subproblem 2
x + 0.3928571429 = -1.467765899 Simplifying x + 0.3928571429 = -1.467765899 Reorder the terms: 0.3928571429 + x = -1.467765899 Solving 0.3928571429 + x = -1.467765899 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 = -1.467765899 + -0.3928571429 Combine like terms: 0.3928571429 + -0.3928571429 = 0.0000000000 0.0000000000 + x = -1.467765899 + -0.3928571429 x = -1.467765899 + -0.3928571429 Combine like terms: -1.467765899 + -0.3928571429 = -1.8606230419 x = -1.8606230419 Simplifying x = -1.8606230419Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0749087561, -1.8606230419}
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