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Simplifying 5x + 2x(x + 10000) = 55000 Reorder the terms: 5x + 2x(10000 + x) = 55000 5x + (10000 * 2x + x * 2x) = 55000 5x + (20000x + 2x2) = 55000 Combine like terms: 5x + 20000x = 20005x 20005x + 2x2 = 55000 Solving 20005x + 2x2 = 55000 Solving for variable 'x'. Reorder the terms: -55000 + 20005x + 2x2 = 55000 + -55000 Combine like terms: 55000 + -55000 = 0 -55000 + 20005x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -27500 + 10002.5x + x2 = 0 Move the constant term to the right: Add '27500' to each side of the equation. -27500 + 10002.5x + 27500 + x2 = 0 + 27500 Reorder the terms: -27500 + 27500 + 10002.5x + x2 = 0 + 27500 Combine like terms: -27500 + 27500 = 0 0 + 10002.5x + x2 = 0 + 27500 10002.5x + x2 = 0 + 27500 Combine like terms: 0 + 27500 = 27500 10002.5x + x2 = 27500 The x term is 10002.5x. Take half its coefficient (5001.25). Square it (25012501.56) and add it to both sides. Add '25012501.56' to each side of the equation. 10002.5x + 25012501.56 + x2 = 27500 + 25012501.56 Reorder the terms: 25012501.56 + 10002.5x + x2 = 27500 + 25012501.56 Combine like terms: 27500 + 25012501.56 = 25040001.56 25012501.56 + 10002.5x + x2 = 25040001.56 Factor a perfect square on the left side: (x + 5001.25)(x + 5001.25) = 25040001.56 Calculate the square root of the right side: 5003.998557154 Break this problem into two subproblems by setting (x + 5001.25) equal to 5003.998557154 and -5003.998557154.Subproblem 1
x + 5001.25 = 5003.998557154 Simplifying x + 5001.25 = 5003.998557154 Reorder the terms: 5001.25 + x = 5003.998557154 Solving 5001.25 + x = 5003.998557154 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5001.25' to each side of the equation. 5001.25 + -5001.25 + x = 5003.998557154 + -5001.25 Combine like terms: 5001.25 + -5001.25 = 0.00 0.00 + x = 5003.998557154 + -5001.25 x = 5003.998557154 + -5001.25 Combine like terms: 5003.998557154 + -5001.25 = 2.748557154 x = 2.748557154 Simplifying x = 2.748557154Subproblem 2
x + 5001.25 = -5003.998557154 Simplifying x + 5001.25 = -5003.998557154 Reorder the terms: 5001.25 + x = -5003.998557154 Solving 5001.25 + x = -5003.998557154 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5001.25' to each side of the equation. 5001.25 + -5001.25 + x = -5003.998557154 + -5001.25 Combine like terms: 5001.25 + -5001.25 = 0.00 0.00 + x = -5003.998557154 + -5001.25 x = -5003.998557154 + -5001.25 Combine like terms: -5003.998557154 + -5001.25 = -10005.248557154 x = -10005.248557154 Simplifying x = -10005.248557154Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.748557154, -10005.248557154}
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