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Simplifying 40 = 0.10x2 + 1.28x + -0.01 Reorder the terms: 40 = -0.01 + 1.28x + 0.10x2 Solving 40 = -0.01 + 1.28x + 0.10x2 Solving for variable 'x'. Combine like terms: 40 + 0.01 = 40.01 40.01 + -1.28x + -0.10x2 = -0.01 + 1.28x + 0.10x2 + 0.01 + -1.28x + -0.10x2 Reorder the terms: 40.01 + -1.28x + -0.10x2 = -0.01 + 0.01 + 1.28x + -1.28x + 0.10x2 + -0.10x2 Combine like terms: -0.01 + 0.01 = 0.00 40.01 + -1.28x + -0.10x2 = 0.00 + 1.28x + -1.28x + 0.10x2 + -0.10x2 40.01 + -1.28x + -0.10x2 = 1.28x + -1.28x + 0.10x2 + -0.10x2 Combine like terms: 1.28x + -1.28x = 0.00 40.01 + -1.28x + -0.10x2 = 0.00 + 0.10x2 + -0.10x2 40.01 + -1.28x + -0.10x2 = 0.10x2 + -0.10x2 Combine like terms: 0.10x2 + -0.10x2 = 0.00 40.01 + -1.28x + -0.10x2 = 0.00 Begin completing the square. Divide all terms by -0.10 the coefficient of the squared term: Divide each side by '-0.10'. -400.1 + 12.8x + x2 = 0 Move the constant term to the right: Add '400.1' to each side of the equation. -400.1 + 12.8x + 400.1 + x2 = 0 + 400.1 Reorder the terms: -400.1 + 400.1 + 12.8x + x2 = 0 + 400.1 Combine like terms: -400.1 + 400.1 = 0.0 0.0 + 12.8x + x2 = 0 + 400.1 12.8x + x2 = 0 + 400.1 Combine like terms: 0 + 400.1 = 400.1 12.8x + x2 = 400.1 The x term is 12.8x. Take half its coefficient (6.4). Square it (40.96) and add it to both sides. Add '40.96' to each side of the equation. 12.8x + 40.96 + x2 = 400.1 + 40.96 Reorder the terms: 40.96 + 12.8x + x2 = 400.1 + 40.96 Combine like terms: 400.1 + 40.96 = 441.06 40.96 + 12.8x + x2 = 441.06 Factor a perfect square on the left side: (x + 6.4)(x + 6.4) = 441.06 Calculate the square root of the right side: 21.001428523 Break this problem into two subproblems by setting (x + 6.4) equal to 21.001428523 and -21.001428523.Subproblem 1
x + 6.4 = 21.001428523 Simplifying x + 6.4 = 21.001428523 Reorder the terms: 6.4 + x = 21.001428523 Solving 6.4 + x = 21.001428523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.4' to each side of the equation. 6.4 + -6.4 + x = 21.001428523 + -6.4 Combine like terms: 6.4 + -6.4 = 0.0 0.0 + x = 21.001428523 + -6.4 x = 21.001428523 + -6.4 Combine like terms: 21.001428523 + -6.4 = 14.601428523 x = 14.601428523 Simplifying x = 14.601428523Subproblem 2
x + 6.4 = -21.001428523 Simplifying x + 6.4 = -21.001428523 Reorder the terms: 6.4 + x = -21.001428523 Solving 6.4 + x = -21.001428523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.4' to each side of the equation. 6.4 + -6.4 + x = -21.001428523 + -6.4 Combine like terms: 6.4 + -6.4 = 0.0 0.0 + x = -21.001428523 + -6.4 x = -21.001428523 + -6.4 Combine like terms: -21.001428523 + -6.4 = -27.401428523 x = -27.401428523 Simplifying x = -27.401428523Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.601428523, -27.401428523}
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