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Simplifying 0 = -21x2 + -30x + 5000 Reorder the terms: 0 = 5000 + -30x + -21x2 Solving 0 = 5000 + -30x + -21x2 Solving for variable 'x'. Combine like terms: 0 + -5000 = -5000 -5000 + 30x + 21x2 = 5000 + -30x + -21x2 + -5000 + 30x + 21x2 Reorder the terms: -5000 + 30x + 21x2 = 5000 + -5000 + -30x + 30x + -21x2 + 21x2 Combine like terms: 5000 + -5000 = 0 -5000 + 30x + 21x2 = 0 + -30x + 30x + -21x2 + 21x2 -5000 + 30x + 21x2 = -30x + 30x + -21x2 + 21x2 Combine like terms: -30x + 30x = 0 -5000 + 30x + 21x2 = 0 + -21x2 + 21x2 -5000 + 30x + 21x2 = -21x2 + 21x2 Combine like terms: -21x2 + 21x2 = 0 -5000 + 30x + 21x2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -238.0952381 + 1.428571429x + x2 = 0 Move the constant term to the right: Add '238.0952381' to each side of the equation. -238.0952381 + 1.428571429x + 238.0952381 + x2 = 0 + 238.0952381 Reorder the terms: -238.0952381 + 238.0952381 + 1.428571429x + x2 = 0 + 238.0952381 Combine like terms: -238.0952381 + 238.0952381 = 0.0000000 0.0000000 + 1.428571429x + x2 = 0 + 238.0952381 1.428571429x + x2 = 0 + 238.0952381 Combine like terms: 0 + 238.0952381 = 238.0952381 1.428571429x + x2 = 238.0952381 The x term is 1.428571429x. Take half its coefficient (0.7142857145). Square it (0.5102040819) and add it to both sides. Add '0.5102040819' to each side of the equation. 1.428571429x + 0.5102040819 + x2 = 238.0952381 + 0.5102040819 Reorder the terms: 0.5102040819 + 1.428571429x + x2 = 238.0952381 + 0.5102040819 Combine like terms: 238.0952381 + 0.5102040819 = 238.6054421819 0.5102040819 + 1.428571429x + x2 = 238.6054421819 Factor a perfect square on the left side: (x + 0.7142857145)(x + 0.7142857145) = 238.6054421819 Calculate the square root of the right side: 15.446858651 Break this problem into two subproblems by setting (x + 0.7142857145) equal to 15.446858651 and -15.446858651.Subproblem 1
x + 0.7142857145 = 15.446858651 Simplifying x + 0.7142857145 = 15.446858651 Reorder the terms: 0.7142857145 + x = 15.446858651 Solving 0.7142857145 + x = 15.446858651 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7142857145' to each side of the equation. 0.7142857145 + -0.7142857145 + x = 15.446858651 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + x = 15.446858651 + -0.7142857145 x = 15.446858651 + -0.7142857145 Combine like terms: 15.446858651 + -0.7142857145 = 14.7325729365 x = 14.7325729365 Simplifying x = 14.7325729365Subproblem 2
x + 0.7142857145 = -15.446858651 Simplifying x + 0.7142857145 = -15.446858651 Reorder the terms: 0.7142857145 + x = -15.446858651 Solving 0.7142857145 + x = -15.446858651 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7142857145' to each side of the equation. 0.7142857145 + -0.7142857145 + x = -15.446858651 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + x = -15.446858651 + -0.7142857145 x = -15.446858651 + -0.7142857145 Combine like terms: -15.446858651 + -0.7142857145 = -16.1611443655 x = -16.1611443655 Simplifying x = -16.1611443655Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.7325729365, -16.1611443655}
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