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Simplifying 3x = 0.01x2 + 0.8x + 40 Reorder the terms: 3x = 40 + 0.8x + 0.01x2 Solving 3x = 40 + 0.8x + 0.01x2 Solving for variable 'x'. Reorder the terms: -40 + 3x + -0.8x + -0.01x2 = 40 + 0.8x + 0.01x2 + -40 + -0.8x + -0.01x2 Combine like terms: 3x + -0.8x = 2.2x -40 + 2.2x + -0.01x2 = 40 + 0.8x + 0.01x2 + -40 + -0.8x + -0.01x2 Reorder the terms: -40 + 2.2x + -0.01x2 = 40 + -40 + 0.8x + -0.8x + 0.01x2 + -0.01x2 Combine like terms: 40 + -40 = 0 -40 + 2.2x + -0.01x2 = 0 + 0.8x + -0.8x + 0.01x2 + -0.01x2 -40 + 2.2x + -0.01x2 = 0.8x + -0.8x + 0.01x2 + -0.01x2 Combine like terms: 0.8x + -0.8x = 0.0 -40 + 2.2x + -0.01x2 = 0.0 + 0.01x2 + -0.01x2 -40 + 2.2x + -0.01x2 = 0.01x2 + -0.01x2 Combine like terms: 0.01x2 + -0.01x2 = 0.00 -40 + 2.2x + -0.01x2 = 0.00 Begin completing the square. Divide all terms by -0.01 the coefficient of the squared term: Divide each side by '-0.01'. 4000 + -220x + x2 = 0 Move the constant term to the right: Add '-4000' to each side of the equation. 4000 + -220x + -4000 + x2 = 0 + -4000 Reorder the terms: 4000 + -4000 + -220x + x2 = 0 + -4000 Combine like terms: 4000 + -4000 = 0 0 + -220x + x2 = 0 + -4000 -220x + x2 = 0 + -4000 Combine like terms: 0 + -4000 = -4000 -220x + x2 = -4000 The x term is -220x. Take half its coefficient (-110). Square it (12100) and add it to both sides. Add '12100' to each side of the equation. -220x + 12100 + x2 = -4000 + 12100 Reorder the terms: 12100 + -220x + x2 = -4000 + 12100 Combine like terms: -4000 + 12100 = 8100 12100 + -220x + x2 = 8100 Factor a perfect square on the left side: (x + -110)(x + -110) = 8100 Calculate the square root of the right side: 90 Break this problem into two subproblems by setting (x + -110) equal to 90 and -90.Subproblem 1
x + -110 = 90 Simplifying x + -110 = 90 Reorder the terms: -110 + x = 90 Solving -110 + x = 90 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '110' to each side of the equation. -110 + 110 + x = 90 + 110 Combine like terms: -110 + 110 = 0 0 + x = 90 + 110 x = 90 + 110 Combine like terms: 90 + 110 = 200 x = 200 Simplifying x = 200Subproblem 2
x + -110 = -90 Simplifying x + -110 = -90 Reorder the terms: -110 + x = -90 Solving -110 + x = -90 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '110' to each side of the equation. -110 + 110 + x = -90 + 110 Combine like terms: -110 + 110 = 0 0 + x = -90 + 110 x = -90 + 110 Combine like terms: -90 + 110 = 20 x = 20 Simplifying x = 20Solution
The solution to the problem is based on the solutions from the subproblems. x = {200, 20}
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