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Simplifying 18.1 = -0.004x * x + x Multiply x * x 18.1 = -0.004x2 + x Reorder the terms: 18.1 = x + -0.004x2 Solving 18.1 = x + -0.004x2 Solving for variable 'x'. Reorder the terms: 18.1 + -1x + 0.004x2 = x + -1x + -0.004x2 + 0.004x2 Combine like terms: x + -1x = 0 18.1 + -1x + 0.004x2 = 0 + -0.004x2 + 0.004x2 18.1 + -1x + 0.004x2 = -0.004x2 + 0.004x2 Combine like terms: -0.004x2 + 0.004x2 = 0.000 18.1 + -1x + 0.004x2 = 0.000 Begin completing the square. Divide all terms by 0.004 the coefficient of the squared term: Divide each side by '0.004'. 4525 + -250x + x2 = 0 Move the constant term to the right: Add '-4525' to each side of the equation. 4525 + -250x + -4525 + x2 = 0 + -4525 Reorder the terms: 4525 + -4525 + -250x + x2 = 0 + -4525 Combine like terms: 4525 + -4525 = 0 0 + -250x + x2 = 0 + -4525 -250x + x2 = 0 + -4525 Combine like terms: 0 + -4525 = -4525 -250x + x2 = -4525 The x term is -250x. Take half its coefficient (-125). Square it (15625) and add it to both sides. Add '15625' to each side of the equation. -250x + 15625 + x2 = -4525 + 15625 Reorder the terms: 15625 + -250x + x2 = -4525 + 15625 Combine like terms: -4525 + 15625 = 11100 15625 + -250x + x2 = 11100 Factor a perfect square on the left side: (x + -125)(x + -125) = 11100 Calculate the square root of the right side: 105.356537529 Break this problem into two subproblems by setting (x + -125) equal to 105.356537529 and -105.356537529.Subproblem 1
x + -125 = 105.356537529 Simplifying x + -125 = 105.356537529 Reorder the terms: -125 + x = 105.356537529 Solving -125 + x = 105.356537529 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '125' to each side of the equation. -125 + 125 + x = 105.356537529 + 125 Combine like terms: -125 + 125 = 0 0 + x = 105.356537529 + 125 x = 105.356537529 + 125 Combine like terms: 105.356537529 + 125 = 230.356537529 x = 230.356537529 Simplifying x = 230.356537529Subproblem 2
x + -125 = -105.356537529 Simplifying x + -125 = -105.356537529 Reorder the terms: -125 + x = -105.356537529 Solving -125 + x = -105.356537529 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '125' to each side of the equation. -125 + 125 + x = -105.356537529 + 125 Combine like terms: -125 + 125 = 0 0 + x = -105.356537529 + 125 x = -105.356537529 + 125 Combine like terms: -105.356537529 + 125 = 19.643462471 x = 19.643462471 Simplifying x = 19.643462471Solution
The solution to the problem is based on the solutions from the subproblems. x = {230.356537529, 19.643462471}
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