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Simplifying -4.9x2 + 14x + -0.4 = 0 Reorder the terms: -0.4 + 14x + -4.9x2 = 0 Solving -0.4 + 14x + -4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. 0.08163265306 + -2.857142857x + x2 = 0 Move the constant term to the right: Add '-0.08163265306' to each side of the equation. 0.08163265306 + -2.857142857x + -0.08163265306 + x2 = 0 + -0.08163265306 Reorder the terms: 0.08163265306 + -0.08163265306 + -2.857142857x + x2 = 0 + -0.08163265306 Combine like terms: 0.08163265306 + -0.08163265306 = 0.00000000000 0.00000000000 + -2.857142857x + x2 = 0 + -0.08163265306 -2.857142857x + x2 = 0 + -0.08163265306 Combine like terms: 0 + -0.08163265306 = -0.08163265306 -2.857142857x + x2 = -0.08163265306 The x term is -2.857142857x. Take half its coefficient (-1.428571429). Square it (2.040816328) and add it to both sides. Add '2.040816328' to each side of the equation. -2.857142857x + 2.040816328 + x2 = -0.08163265306 + 2.040816328 Reorder the terms: 2.040816328 + -2.857142857x + x2 = -0.08163265306 + 2.040816328 Combine like terms: -0.08163265306 + 2.040816328 = 1.95918367494 2.040816328 + -2.857142857x + x2 = 1.95918367494 Factor a perfect square on the left side: (x + -1.428571429)(x + -1.428571429) = 1.95918367494 Calculate the square root of the right side: 1.399708425 Break this problem into two subproblems by setting (x + -1.428571429) equal to 1.399708425 and -1.399708425.Subproblem 1
x + -1.428571429 = 1.399708425 Simplifying x + -1.428571429 = 1.399708425 Reorder the terms: -1.428571429 + x = 1.399708425 Solving -1.428571429 + x = 1.399708425 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + x = 1.399708425 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + x = 1.399708425 + 1.428571429 x = 1.399708425 + 1.428571429 Combine like terms: 1.399708425 + 1.428571429 = 2.828279854 x = 2.828279854 Simplifying x = 2.828279854Subproblem 2
x + -1.428571429 = -1.399708425 Simplifying x + -1.428571429 = -1.399708425 Reorder the terms: -1.428571429 + x = -1.399708425 Solving -1.428571429 + x = -1.399708425 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + x = -1.399708425 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + x = -1.399708425 + 1.428571429 x = -1.399708425 + 1.428571429 Combine like terms: -1.399708425 + 1.428571429 = 0.028863004 x = 0.028863004 Simplifying x = 0.028863004Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.828279854, 0.028863004}
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