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Simplifying 460.1x2 + 368.08x + 14.3 = 0 Reorder the terms: 14.3 + 368.08x + 460.1x2 = 0 Solving 14.3 + 368.08x + 460.1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 460.1 the coefficient of the squared term: Divide each side by '460.1'. 0.03108019996 + 0.8x + x2 = 0 Move the constant term to the right: Add '-0.03108019996' to each side of the equation. 0.03108019996 + 0.8x + -0.03108019996 + x2 = 0 + -0.03108019996 Reorder the terms: 0.03108019996 + -0.03108019996 + 0.8x + x2 = 0 + -0.03108019996 Combine like terms: 0.03108019996 + -0.03108019996 = 0.00000000000 0.00000000000 + 0.8x + x2 = 0 + -0.03108019996 0.8x + x2 = 0 + -0.03108019996 Combine like terms: 0 + -0.03108019996 = -0.03108019996 0.8x + x2 = -0.03108019996 The x term is 0.8x. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8x + 0.16 + x2 = -0.03108019996 + 0.16 Reorder the terms: 0.16 + 0.8x + x2 = -0.03108019996 + 0.16 Combine like terms: -0.03108019996 + 0.16 = 0.12891980004 0.16 + 0.8x + x2 = 0.12891980004 Factor a perfect square on the left side: (x + 0.4)(x + 0.4) = 0.12891980004 Calculate the square root of the right side: 0.359054035 Break this problem into two subproblems by setting (x + 0.4) equal to 0.359054035 and -0.359054035.Subproblem 1
x + 0.4 = 0.359054035 Simplifying x + 0.4 = 0.359054035 Reorder the terms: 0.4 + x = 0.359054035 Solving 0.4 + x = 0.359054035 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = 0.359054035 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = 0.359054035 + -0.4 x = 0.359054035 + -0.4 Combine like terms: 0.359054035 + -0.4 = -0.040945965 x = -0.040945965 Simplifying x = -0.040945965Subproblem 2
x + 0.4 = -0.359054035 Simplifying x + 0.4 = -0.359054035 Reorder the terms: 0.4 + x = -0.359054035 Solving 0.4 + x = -0.359054035 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = -0.359054035 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = -0.359054035 + -0.4 x = -0.359054035 + -0.4 Combine like terms: -0.359054035 + -0.4 = -0.759054035 x = -0.759054035 Simplifying x = -0.759054035Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.040945965, -0.759054035}
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