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Simplifying 0.1x2 + 5x = 6000 Reorder the terms: 5x + 0.1x2 = 6000 Solving 5x + 0.1x2 = 6000 Solving for variable 'x'. Reorder the terms: -6000 + 5x + 0.1x2 = 6000 + -6000 Combine like terms: 6000 + -6000 = 0 -6000 + 5x + 0.1x2 = 0 Begin completing the square. Divide all terms by 0.1 the coefficient of the squared term: Divide each side by '0.1'. -60000 + 50x + x2 = 0 Move the constant term to the right: Add '60000' to each side of the equation. -60000 + 50x + 60000 + x2 = 0 + 60000 Reorder the terms: -60000 + 60000 + 50x + x2 = 0 + 60000 Combine like terms: -60000 + 60000 = 0 0 + 50x + x2 = 0 + 60000 50x + x2 = 0 + 60000 Combine like terms: 0 + 60000 = 60000 50x + x2 = 60000 The x term is 50x. Take half its coefficient (25). Square it (625) and add it to both sides. Add '625' to each side of the equation. 50x + 625 + x2 = 60000 + 625 Reorder the terms: 625 + 50x + x2 = 60000 + 625 Combine like terms: 60000 + 625 = 60625 625 + 50x + x2 = 60625 Factor a perfect square on the left side: (x + 25)(x + 25) = 60625 Calculate the square root of the right side: 246.221445045 Break this problem into two subproblems by setting (x + 25) equal to 246.221445045 and -246.221445045.Subproblem 1
x + 25 = 246.221445045 Simplifying x + 25 = 246.221445045 Reorder the terms: 25 + x = 246.221445045 Solving 25 + x = 246.221445045 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = 246.221445045 + -25 Combine like terms: 25 + -25 = 0 0 + x = 246.221445045 + -25 x = 246.221445045 + -25 Combine like terms: 246.221445045 + -25 = 221.221445045 x = 221.221445045 Simplifying x = 221.221445045Subproblem 2
x + 25 = -246.221445045 Simplifying x + 25 = -246.221445045 Reorder the terms: 25 + x = -246.221445045 Solving 25 + x = -246.221445045 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = -246.221445045 + -25 Combine like terms: 25 + -25 = 0 0 + x = -246.221445045 + -25 x = -246.221445045 + -25 Combine like terms: -246.221445045 + -25 = -271.221445045 x = -271.221445045 Simplifying x = -271.221445045Solution
The solution to the problem is based on the solutions from the subproblems. x = {221.221445045, -271.221445045}
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