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Simplifying 0.167x2 + 0.096x + -0.476 = 0 Reorder the terms: -0.476 + 0.096x + 0.167x2 = 0 Solving -0.476 + 0.096x + 0.167x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.167 the coefficient of the squared term: Divide each side by '0.167'. -2.850299401 + 0.5748502994x + x2 = 0 Move the constant term to the right: Add '2.850299401' to each side of the equation. -2.850299401 + 0.5748502994x + 2.850299401 + x2 = 0 + 2.850299401 Reorder the terms: -2.850299401 + 2.850299401 + 0.5748502994x + x2 = 0 + 2.850299401 Combine like terms: -2.850299401 + 2.850299401 = 0.000000000 0.000000000 + 0.5748502994x + x2 = 0 + 2.850299401 0.5748502994x + x2 = 0 + 2.850299401 Combine like terms: 0 + 2.850299401 = 2.850299401 0.5748502994x + x2 = 2.850299401 The x term is 0.5748502994x. Take half its coefficient (0.2874251497). Square it (0.08261321668) and add it to both sides. Add '0.08261321668' to each side of the equation. 0.5748502994x + 0.08261321668 + x2 = 2.850299401 + 0.08261321668 Reorder the terms: 0.08261321668 + 0.5748502994x + x2 = 2.850299401 + 0.08261321668 Combine like terms: 2.850299401 + 0.08261321668 = 2.93291261768 0.08261321668 + 0.5748502994x + x2 = 2.93291261768 Factor a perfect square on the left side: (x + 0.2874251497)(x + 0.2874251497) = 2.93291261768 Calculate the square root of the right side: 1.71257485 Break this problem into two subproblems by setting (x + 0.2874251497) equal to 1.71257485 and -1.71257485.Subproblem 1
x + 0.2874251497 = 1.71257485 Simplifying x + 0.2874251497 = 1.71257485 Reorder the terms: 0.2874251497 + x = 1.71257485 Solving 0.2874251497 + x = 1.71257485 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2874251497' to each side of the equation. 0.2874251497 + -0.2874251497 + x = 1.71257485 + -0.2874251497 Combine like terms: 0.2874251497 + -0.2874251497 = 0.0000000000 0.0000000000 + x = 1.71257485 + -0.2874251497 x = 1.71257485 + -0.2874251497 Combine like terms: 1.71257485 + -0.2874251497 = 1.4251497003 x = 1.4251497003 Simplifying x = 1.4251497003Subproblem 2
x + 0.2874251497 = -1.71257485 Simplifying x + 0.2874251497 = -1.71257485 Reorder the terms: 0.2874251497 + x = -1.71257485 Solving 0.2874251497 + x = -1.71257485 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2874251497' to each side of the equation. 0.2874251497 + -0.2874251497 + x = -1.71257485 + -0.2874251497 Combine like terms: 0.2874251497 + -0.2874251497 = 0.0000000000 0.0000000000 + x = -1.71257485 + -0.2874251497 x = -1.71257485 + -0.2874251497 Combine like terms: -1.71257485 + -0.2874251497 = -1.9999999997 x = -1.9999999997 Simplifying x = -1.9999999997Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4251497003, -1.9999999997}
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