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Simplifying 0.04x2 + -3x + 44 = 0 Reorder the terms: 44 + -3x + 0.04x2 = 0 Solving 44 + -3x + 0.04x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.04 the coefficient of the squared term: Divide each side by '0.04'. 1100 + -75x + x2 = 0 Move the constant term to the right: Add '-1100' to each side of the equation. 1100 + -75x + -1100 + x2 = 0 + -1100 Reorder the terms: 1100 + -1100 + -75x + x2 = 0 + -1100 Combine like terms: 1100 + -1100 = 0 0 + -75x + x2 = 0 + -1100 -75x + x2 = 0 + -1100 Combine like terms: 0 + -1100 = -1100 -75x + x2 = -1100 The x term is -75x. Take half its coefficient (-37.5). Square it (1406.25) and add it to both sides. Add '1406.25' to each side of the equation. -75x + 1406.25 + x2 = -1100 + 1406.25 Reorder the terms: 1406.25 + -75x + x2 = -1100 + 1406.25 Combine like terms: -1100 + 1406.25 = 306.25 1406.25 + -75x + x2 = 306.25 Factor a perfect square on the left side: (x + -37.5)(x + -37.5) = 306.25 Calculate the square root of the right side: 17.5 Break this problem into two subproblems by setting (x + -37.5) equal to 17.5 and -17.5.Subproblem 1
x + -37.5 = 17.5 Simplifying x + -37.5 = 17.5 Reorder the terms: -37.5 + x = 17.5 Solving -37.5 + x = 17.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '37.5' to each side of the equation. -37.5 + 37.5 + x = 17.5 + 37.5 Combine like terms: -37.5 + 37.5 = 0.0 0.0 + x = 17.5 + 37.5 x = 17.5 + 37.5 Combine like terms: 17.5 + 37.5 = 55 x = 55 Simplifying x = 55Subproblem 2
x + -37.5 = -17.5 Simplifying x + -37.5 = -17.5 Reorder the terms: -37.5 + x = -17.5 Solving -37.5 + x = -17.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '37.5' to each side of the equation. -37.5 + 37.5 + x = -17.5 + 37.5 Combine like terms: -37.5 + 37.5 = 0.0 0.0 + x = -17.5 + 37.5 x = -17.5 + 37.5 Combine like terms: -17.5 + 37.5 = 20 x = 20 Simplifying x = 20Solution
The solution to the problem is based on the solutions from the subproblems. x = {55, 20}
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