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Simplifying 0.04x2 + -3.5x + 100 = 60 Reorder the terms: 100 + -3.5x + 0.04x2 = 60 Solving 100 + -3.5x + 0.04x2 = 60 Solving for variable 'x'. Reorder the terms: 100 + -60 + -3.5x + 0.04x2 = 60 + -60 Combine like terms: 100 + -60 = 40 40 + -3.5x + 0.04x2 = 60 + -60 Combine like terms: 60 + -60 = 0 40 + -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'. 1000 + -87.5x + x2 = 0 Move the constant term to the right: Add '-1000' to each side of the equation. 1000 + -87.5x + -1000 + x2 = 0 + -1000 Reorder the terms: 1000 + -1000 + -87.5x + x2 = 0 + -1000 Combine like terms: 1000 + -1000 = 0 0 + -87.5x + x2 = 0 + -1000 -87.5x + x2 = 0 + -1000 Combine like terms: 0 + -1000 = -1000 -87.5x + x2 = -1000 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 = -1000 + 1914.0625 Reorder the terms: 1914.0625 + -87.5x + x2 = -1000 + 1914.0625 Combine like terms: -1000 + 1914.0625 = 914.0625 1914.0625 + -87.5x + x2 = 914.0625 Factor a perfect square on the left side: (x + -43.75)(x + -43.75) = 914.0625 Calculate the square root of the right side: 30.233466556 Break this problem into two subproblems by setting (x + -43.75) equal to 30.233466556 and -30.233466556.Subproblem 1
x + -43.75 = 30.233466556 Simplifying x + -43.75 = 30.233466556 Reorder the terms: -43.75 + x = 30.233466556 Solving -43.75 + x = 30.233466556 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 = 30.233466556 + 43.75 Combine like terms: -43.75 + 43.75 = 0.00 0.00 + x = 30.233466556 + 43.75 x = 30.233466556 + 43.75 Combine like terms: 30.233466556 + 43.75 = 73.983466556 x = 73.983466556 Simplifying x = 73.983466556Subproblem 2
x + -43.75 = -30.233466556 Simplifying x + -43.75 = -30.233466556 Reorder the terms: -43.75 + x = -30.233466556 Solving -43.75 + x = -30.233466556 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 = -30.233466556 + 43.75 Combine like terms: -43.75 + 43.75 = 0.00 0.00 + x = -30.233466556 + 43.75 x = -30.233466556 + 43.75 Combine like terms: -30.233466556 + 43.75 = 13.516533444 x = 13.516533444 Simplifying x = 13.516533444Solution
The solution to the problem is based on the solutions from the subproblems. x = {73.983466556, 13.516533444}
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