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Simplifying 26.3 = -0.004x * x + x Multiply x * x 26.3 = -0.004x2 + x Reorder the terms: 26.3 = x + -0.004x2 Solving 26.3 = x + -0.004x2 Solving for variable 'x'. Reorder the terms: 26.3 + -1x + 0.004x2 = x + -1x + -0.004x2 + 0.004x2 Combine like terms: x + -1x = 0 26.3 + -1x + 0.004x2 = 0 + -0.004x2 + 0.004x2 26.3 + -1x + 0.004x2 = -0.004x2 + 0.004x2 Combine like terms: -0.004x2 + 0.004x2 = 0.000 26.3 + -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'. 6575 + -250x + x2 = 0 Move the constant term to the right: Add '-6575' to each side of the equation. 6575 + -250x + -6575 + x2 = 0 + -6575 Reorder the terms: 6575 + -6575 + -250x + x2 = 0 + -6575 Combine like terms: 6575 + -6575 = 0 0 + -250x + x2 = 0 + -6575 -250x + x2 = 0 + -6575 Combine like terms: 0 + -6575 = -6575 -250x + x2 = -6575 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 = -6575 + 15625 Reorder the terms: 15625 + -250x + x2 = -6575 + 15625 Combine like terms: -6575 + 15625 = 9050 15625 + -250x + x2 = 9050 Factor a perfect square on the left side: (x + -125)(x + -125) = 9050 Calculate the square root of the right side: 95.131487952 Break this problem into two subproblems by setting (x + -125) equal to 95.131487952 and -95.131487952.Subproblem 1
x + -125 = 95.131487952 Simplifying x + -125 = 95.131487952 Reorder the terms: -125 + x = 95.131487952 Solving -125 + x = 95.131487952 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 = 95.131487952 + 125 Combine like terms: -125 + 125 = 0 0 + x = 95.131487952 + 125 x = 95.131487952 + 125 Combine like terms: 95.131487952 + 125 = 220.131487952 x = 220.131487952 Simplifying x = 220.131487952Subproblem 2
x + -125 = -95.131487952 Simplifying x + -125 = -95.131487952 Reorder the terms: -125 + x = -95.131487952 Solving -125 + x = -95.131487952 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 = -95.131487952 + 125 Combine like terms: -125 + 125 = 0 0 + x = -95.131487952 + 125 x = -95.131487952 + 125 Combine like terms: -95.131487952 + 125 = 29.868512048 x = 29.868512048 Simplifying x = 29.868512048Solution
The solution to the problem is based on the solutions from the subproblems. x = {220.131487952, 29.868512048}
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