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Simplifying 4.9x2 + 9.1x + 1.4 = 0 Reorder the terms: 1.4 + 9.1x + 4.9x2 = 0 Solving 1.4 + 9.1x + 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'. 0.2857142857 + 1.857142857x + x2 = 0 Move the constant term to the right: Add '-0.2857142857' to each side of the equation. 0.2857142857 + 1.857142857x + -0.2857142857 + x2 = 0 + -0.2857142857 Reorder the terms: 0.2857142857 + -0.2857142857 + 1.857142857x + x2 = 0 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + 1.857142857x + x2 = 0 + -0.2857142857 1.857142857x + x2 = 0 + -0.2857142857 Combine like terms: 0 + -0.2857142857 = -0.2857142857 1.857142857x + x2 = -0.2857142857 The x term is 1.857142857x. Take half its coefficient (0.9285714285). Square it (0.8622448978) and add it to both sides. Add '0.8622448978' to each side of the equation. 1.857142857x + 0.8622448978 + x2 = -0.2857142857 + 0.8622448978 Reorder the terms: 0.8622448978 + 1.857142857x + x2 = -0.2857142857 + 0.8622448978 Combine like terms: -0.2857142857 + 0.8622448978 = 0.5765306121 0.8622448978 + 1.857142857x + x2 = 0.5765306121 Factor a perfect square on the left side: (x + 0.9285714285)(x + 0.9285714285) = 0.5765306121 Calculate the square root of the right side: 0.759296129 Break this problem into two subproblems by setting (x + 0.9285714285) equal to 0.759296129 and -0.759296129.Subproblem 1
x + 0.9285714285 = 0.759296129 Simplifying x + 0.9285714285 = 0.759296129 Reorder the terms: 0.9285714285 + x = 0.759296129 Solving 0.9285714285 + x = 0.759296129 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9285714285' to each side of the equation. 0.9285714285 + -0.9285714285 + x = 0.759296129 + -0.9285714285 Combine like terms: 0.9285714285 + -0.9285714285 = 0.0000000000 0.0000000000 + x = 0.759296129 + -0.9285714285 x = 0.759296129 + -0.9285714285 Combine like terms: 0.759296129 + -0.9285714285 = -0.1692752995 x = -0.1692752995 Simplifying x = -0.1692752995Subproblem 2
x + 0.9285714285 = -0.759296129 Simplifying x + 0.9285714285 = -0.759296129 Reorder the terms: 0.9285714285 + x = -0.759296129 Solving 0.9285714285 + x = -0.759296129 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9285714285' to each side of the equation. 0.9285714285 + -0.9285714285 + x = -0.759296129 + -0.9285714285 Combine like terms: 0.9285714285 + -0.9285714285 = 0.0000000000 0.0000000000 + x = -0.759296129 + -0.9285714285 x = -0.759296129 + -0.9285714285 Combine like terms: -0.759296129 + -0.9285714285 = -1.6878675575 x = -1.6878675575 Simplifying x = -1.6878675575Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.1692752995, -1.6878675575}
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