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Simplifying 0.149x2 + 0.083x + -0.494 = 0 Reorder the terms: -0.494 + 0.083x + 0.149x2 = 0 Solving -0.494 + 0.083x + 0.149x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.149 the coefficient of the squared term: Divide each side by '0.149'. -3.315436242 + 0.5570469799x + x2 = 0 Move the constant term to the right: Add '3.315436242' to each side of the equation. -3.315436242 + 0.5570469799x + 3.315436242 + x2 = 0 + 3.315436242 Reorder the terms: -3.315436242 + 3.315436242 + 0.5570469799x + x2 = 0 + 3.315436242 Combine like terms: -3.315436242 + 3.315436242 = 0.000000000 0.000000000 + 0.5570469799x + x2 = 0 + 3.315436242 0.5570469799x + x2 = 0 + 3.315436242 Combine like terms: 0 + 3.315436242 = 3.315436242 0.5570469799x + x2 = 3.315436242 The x term is 0.5570469799x. Take half its coefficient (0.27852349). Square it (0.07757533448) and add it to both sides. Add '0.07757533448' to each side of the equation. 0.5570469799x + 0.07757533448 + x2 = 3.315436242 + 0.07757533448 Reorder the terms: 0.07757533448 + 0.5570469799x + x2 = 3.315436242 + 0.07757533448 Combine like terms: 3.315436242 + 0.07757533448 = 3.39301157648 0.07757533448 + 0.5570469799x + x2 = 3.39301157648 Factor a perfect square on the left side: (x + 0.27852349)(x + 0.27852349) = 3.39301157648 Calculate the square root of the right side: 1.842012914 Break this problem into two subproblems by setting (x + 0.27852349) equal to 1.842012914 and -1.842012914.Subproblem 1
x + 0.27852349 = 1.842012914 Simplifying x + 0.27852349 = 1.842012914 Reorder the terms: 0.27852349 + x = 1.842012914 Solving 0.27852349 + x = 1.842012914 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.27852349' to each side of the equation. 0.27852349 + -0.27852349 + x = 1.842012914 + -0.27852349 Combine like terms: 0.27852349 + -0.27852349 = 0.00000000 0.00000000 + x = 1.842012914 + -0.27852349 x = 1.842012914 + -0.27852349 Combine like terms: 1.842012914 + -0.27852349 = 1.563489424 x = 1.563489424 Simplifying x = 1.563489424Subproblem 2
x + 0.27852349 = -1.842012914 Simplifying x + 0.27852349 = -1.842012914 Reorder the terms: 0.27852349 + x = -1.842012914 Solving 0.27852349 + x = -1.842012914 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.27852349' to each side of the equation. 0.27852349 + -0.27852349 + x = -1.842012914 + -0.27852349 Combine like terms: 0.27852349 + -0.27852349 = 0.00000000 0.00000000 + x = -1.842012914 + -0.27852349 x = -1.842012914 + -0.27852349 Combine like terms: -1.842012914 + -0.27852349 = -2.120536404 x = -2.120536404 Simplifying x = -2.120536404Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.563489424, -2.120536404}
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