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Simplifying 28x2 + 4x + -385 = 0 Reorder the terms: -385 + 4x + 28x2 = 0 Solving -385 + 4x + 28x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 28 the coefficient of the squared term: Divide each side by '28'. -13.75 + 0.1428571429x + x2 = 0 Move the constant term to the right: Add '13.75' to each side of the equation. -13.75 + 0.1428571429x + 13.75 + x2 = 0 + 13.75 Reorder the terms: -13.75 + 13.75 + 0.1428571429x + x2 = 0 + 13.75 Combine like terms: -13.75 + 13.75 = 0.00 0.00 + 0.1428571429x + x2 = 0 + 13.75 0.1428571429x + x2 = 0 + 13.75 Combine like terms: 0 + 13.75 = 13.75 0.1428571429x + x2 = 13.75 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 = 13.75 + 0.005102040819 Reorder the terms: 0.005102040819 + 0.1428571429x + x2 = 13.75 + 0.005102040819 Combine like terms: 13.75 + 0.005102040819 = 13.755102040819 0.005102040819 + 0.1428571429x + x2 = 13.755102040819 Factor a perfect square on the left side: (x + 0.07142857145)(x + 0.07142857145) = 13.755102040819 Calculate the square root of the right side: 3.708787139 Break this problem into two subproblems by setting (x + 0.07142857145) equal to 3.708787139 and -3.708787139.Subproblem 1
x + 0.07142857145 = 3.708787139 Simplifying x + 0.07142857145 = 3.708787139 Reorder the terms: 0.07142857145 + x = 3.708787139 Solving 0.07142857145 + x = 3.708787139 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 = 3.708787139 + -0.07142857145 Combine like terms: 0.07142857145 + -0.07142857145 = 0.00000000000 0.00000000000 + x = 3.708787139 + -0.07142857145 x = 3.708787139 + -0.07142857145 Combine like terms: 3.708787139 + -0.07142857145 = 3.63735856755 x = 3.63735856755 Simplifying x = 3.63735856755Subproblem 2
x + 0.07142857145 = -3.708787139 Simplifying x + 0.07142857145 = -3.708787139 Reorder the terms: 0.07142857145 + x = -3.708787139 Solving 0.07142857145 + x = -3.708787139 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 = -3.708787139 + -0.07142857145 Combine like terms: 0.07142857145 + -0.07142857145 = 0.00000000000 0.00000000000 + x = -3.708787139 + -0.07142857145 x = -3.708787139 + -0.07142857145 Combine like terms: -3.708787139 + -0.07142857145 = -3.78021571045 x = -3.78021571045 Simplifying x = -3.78021571045Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.63735856755, -3.78021571045}
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