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Simplifying 0.2x2 + 105x + -2500 = 0 Reorder the terms: -2500 + 105x + 0.2x2 = 0 Solving -2500 + 105x + 0.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. -12500 + 525x + x2 = 0 Move the constant term to the right: Add '12500' to each side of the equation. -12500 + 525x + 12500 + x2 = 0 + 12500 Reorder the terms: -12500 + 12500 + 525x + x2 = 0 + 12500 Combine like terms: -12500 + 12500 = 0 0 + 525x + x2 = 0 + 12500 525x + x2 = 0 + 12500 Combine like terms: 0 + 12500 = 12500 525x + x2 = 12500 The x term is 525x. Take half its coefficient (262.5). Square it (68906.25) and add it to both sides. Add '68906.25' to each side of the equation. 525x + 68906.25 + x2 = 12500 + 68906.25 Reorder the terms: 68906.25 + 525x + x2 = 12500 + 68906.25 Combine like terms: 12500 + 68906.25 = 81406.25 68906.25 + 525x + x2 = 81406.25 Factor a perfect square on the left side: (x + 262.5)(x + 262.5) = 81406.25 Calculate the square root of the right side: 285.317805263 Break this problem into two subproblems by setting (x + 262.5) equal to 285.317805263 and -285.317805263.Subproblem 1
x + 262.5 = 285.317805263 Simplifying x + 262.5 = 285.317805263 Reorder the terms: 262.5 + x = 285.317805263 Solving 262.5 + x = 285.317805263 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-262.5' to each side of the equation. 262.5 + -262.5 + x = 285.317805263 + -262.5 Combine like terms: 262.5 + -262.5 = 0.0 0.0 + x = 285.317805263 + -262.5 x = 285.317805263 + -262.5 Combine like terms: 285.317805263 + -262.5 = 22.817805263 x = 22.817805263 Simplifying x = 22.817805263Subproblem 2
x + 262.5 = -285.317805263 Simplifying x + 262.5 = -285.317805263 Reorder the terms: 262.5 + x = -285.317805263 Solving 262.5 + x = -285.317805263 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-262.5' to each side of the equation. 262.5 + -262.5 + x = -285.317805263 + -262.5 Combine like terms: 262.5 + -262.5 = 0.0 0.0 + x = -285.317805263 + -262.5 x = -285.317805263 + -262.5 Combine like terms: -285.317805263 + -262.5 = -547.817805263 x = -547.817805263 Simplifying x = -547.817805263Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.817805263, -547.817805263}
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