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Simplifying (x) = -0.3x2 + 75x + -2000 x = -0.3x2 + 75x + -2000 Reorder the terms: x = -2000 + 75x + -0.3x2 Solving x = -2000 + 75x + -0.3x2 Solving for variable 'x'. Reorder the terms: 2000 + x + -75x + 0.3x2 = -2000 + 75x + -0.3x2 + 2000 + -75x + 0.3x2 Combine like terms: x + -75x = -74x 2000 + -74x + 0.3x2 = -2000 + 75x + -0.3x2 + 2000 + -75x + 0.3x2 Reorder the terms: 2000 + -74x + 0.3x2 = -2000 + 2000 + 75x + -75x + -0.3x2 + 0.3x2 Combine like terms: -2000 + 2000 = 0 2000 + -74x + 0.3x2 = 0 + 75x + -75x + -0.3x2 + 0.3x2 2000 + -74x + 0.3x2 = 75x + -75x + -0.3x2 + 0.3x2 Combine like terms: 75x + -75x = 0 2000 + -74x + 0.3x2 = 0 + -0.3x2 + 0.3x2 2000 + -74x + 0.3x2 = -0.3x2 + 0.3x2 Combine like terms: -0.3x2 + 0.3x2 = 0.0 2000 + -74x + 0.3x2 = 0.0 Begin completing the square. Divide all terms by 0.3 the coefficient of the squared term: Divide each side by '0.3'. 6666.666667 + -246.6666667x + x2 = 0 Move the constant term to the right: Add '-6666.666667' to each side of the equation. 6666.666667 + -246.6666667x + -6666.666667 + x2 = 0 + -6666.666667 Reorder the terms: 6666.666667 + -6666.666667 + -246.6666667x + x2 = 0 + -6666.666667 Combine like terms: 6666.666667 + -6666.666667 = 0.000000 0.000000 + -246.6666667x + x2 = 0 + -6666.666667 -246.6666667x + x2 = 0 + -6666.666667 Combine like terms: 0 + -6666.666667 = -6666.666667 -246.6666667x + x2 = -6666.666667 The x term is -246.6666667x. Take half its coefficient (-123.3333334). Square it (15211.11113) and add it to both sides. Add '15211.11113' to each side of the equation. -246.6666667x + 15211.11113 + x2 = -6666.666667 + 15211.11113 Reorder the terms: 15211.11113 + -246.6666667x + x2 = -6666.666667 + 15211.11113 Combine like terms: -6666.666667 + 15211.11113 = 8544.444463 15211.11113 + -246.6666667x + x2 = 8544.444463 Factor a perfect square on the left side: (x + -123.3333334)(x + -123.3333334) = 8544.444463 Calculate the square root of the right side: 92.436164259 Break this problem into two subproblems by setting (x + -123.3333334) equal to 92.436164259 and -92.436164259.Subproblem 1
x + -123.3333334 = 92.436164259 Simplifying x + -123.3333334 = 92.436164259 Reorder the terms: -123.3333334 + x = 92.436164259 Solving -123.3333334 + x = 92.436164259 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '123.3333334' to each side of the equation. -123.3333334 + 123.3333334 + x = 92.436164259 + 123.3333334 Combine like terms: -123.3333334 + 123.3333334 = 0.0000000 0.0000000 + x = 92.436164259 + 123.3333334 x = 92.436164259 + 123.3333334 Combine like terms: 92.436164259 + 123.3333334 = 215.769497659 x = 215.769497659 Simplifying x = 215.769497659Subproblem 2
x + -123.3333334 = -92.436164259 Simplifying x + -123.3333334 = -92.436164259 Reorder the terms: -123.3333334 + x = -92.436164259 Solving -123.3333334 + x = -92.436164259 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '123.3333334' to each side of the equation. -123.3333334 + 123.3333334 + x = -92.436164259 + 123.3333334 Combine like terms: -123.3333334 + 123.3333334 = 0.0000000 0.0000000 + x = -92.436164259 + 123.3333334 x = -92.436164259 + 123.3333334 Combine like terms: -92.436164259 + 123.3333334 = 30.897169141 x = 30.897169141 Simplifying x = 30.897169141Solution
The solution to the problem is based on the solutions from the subproblems. x = {215.769497659, 30.897169141}
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