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Simplifying 0.04x2 + -3.5x + 100 = 40 Reorder the terms: 100 + -3.5x + 0.04x2 = 40 Solving 100 + -3.5x + 0.04x2 = 40 Solving for variable 'x'. Reorder the terms: 100 + -40 + -3.5x + 0.04x2 = 40 + -40 Combine like terms: 100 + -40 = 60 60 + -3.5x + 0.04x2 = 40 + -40 Combine like terms: 40 + -40 = 0 60 + -3.5x + 0.04x2 = 0 Begin completing the square. Divide all terms by 0.04 the coefficient of the squared term: Divide each side by '0.04'. 1500 + -87.5x + x2 = 0 Move the constant term to the right: Add '-1500' to each side of the equation. 1500 + -87.5x + -1500 + x2 = 0 + -1500 Reorder the terms: 1500 + -1500 + -87.5x + x2 = 0 + -1500 Combine like terms: 1500 + -1500 = 0 0 + -87.5x + x2 = 0 + -1500 -87.5x + x2 = 0 + -1500 Combine like terms: 0 + -1500 = -1500 -87.5x + x2 = -1500 The x term is -87.5x. Take half its coefficient (-43.75). Square it (1914.0625) and add it to both sides. Add '1914.0625' to each side of the equation. -87.5x + 1914.0625 + x2 = -1500 + 1914.0625 Reorder the terms: 1914.0625 + -87.5x + x2 = -1500 + 1914.0625 Combine like terms: -1500 + 1914.0625 = 414.0625 1914.0625 + -87.5x + x2 = 414.0625 Factor a perfect square on the left side: (x + -43.75)(x + -43.75) = 414.0625 Calculate the square root of the right side: 20.348525745 Break this problem into two subproblems by setting (x + -43.75) equal to 20.348525745 and -20.348525745.Subproblem 1
x + -43.75 = 20.348525745 Simplifying x + -43.75 = 20.348525745 Reorder the terms: -43.75 + x = 20.348525745 Solving -43.75 + x = 20.348525745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '43.75' to each side of the equation. -43.75 + 43.75 + x = 20.348525745 + 43.75 Combine like terms: -43.75 + 43.75 = 0.00 0.00 + x = 20.348525745 + 43.75 x = 20.348525745 + 43.75 Combine like terms: 20.348525745 + 43.75 = 64.098525745 x = 64.098525745 Simplifying x = 64.098525745Subproblem 2
x + -43.75 = -20.348525745 Simplifying x + -43.75 = -20.348525745 Reorder the terms: -43.75 + x = -20.348525745 Solving -43.75 + x = -20.348525745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '43.75' to each side of the equation. -43.75 + 43.75 + x = -20.348525745 + 43.75 Combine like terms: -43.75 + 43.75 = 0.00 0.00 + x = -20.348525745 + 43.75 x = -20.348525745 + 43.75 Combine like terms: -20.348525745 + 43.75 = 23.401474255 x = 23.401474255 Simplifying x = 23.401474255Solution
The solution to the problem is based on the solutions from the subproblems. x = {64.098525745, 23.401474255}
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