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Simplifying 20x + 50x2 = 25200 Solving 20x + 50x2 = 25200 Solving for variable 'x'. Reorder the terms: -25200 + 20x + 50x2 = 25200 + -25200 Combine like terms: 25200 + -25200 = 0 -25200 + 20x + 50x2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(-2520 + 2x + 5x2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-2520 + 2x + 5x2)' equal to zero and attempt to solve: Simplifying -2520 + 2x + 5x2 = 0 Solving -2520 + 2x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -504 + 0.4x + x2 = 0 Move the constant term to the right: Add '504' to each side of the equation. -504 + 0.4x + 504 + x2 = 0 + 504 Reorder the terms: -504 + 504 + 0.4x + x2 = 0 + 504 Combine like terms: -504 + 504 = 0 0 + 0.4x + x2 = 0 + 504 0.4x + x2 = 0 + 504 Combine like terms: 0 + 504 = 504 0.4x + x2 = 504 The x term is 0.4x. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4x + 0.04 + x2 = 504 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 504 + 0.04 Combine like terms: 504 + 0.04 = 504.04 0.04 + 0.4x + x2 = 504.04 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 504.04 Calculate the square root of the right side: 22.450835174 Break this problem into two subproblems by setting (x + 0.2) equal to 22.450835174 and -22.450835174.Subproblem 1
x + 0.2 = 22.450835174 Simplifying x + 0.2 = 22.450835174 Reorder the terms: 0.2 + x = 22.450835174 Solving 0.2 + x = 22.450835174 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 22.450835174 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 22.450835174 + -0.2 x = 22.450835174 + -0.2 Combine like terms: 22.450835174 + -0.2 = 22.250835174 x = 22.250835174 Simplifying x = 22.250835174Subproblem 2
x + 0.2 = -22.450835174 Simplifying x + 0.2 = -22.450835174 Reorder the terms: 0.2 + x = -22.450835174 Solving 0.2 + x = -22.450835174 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = -22.450835174 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -22.450835174 + -0.2 x = -22.450835174 + -0.2 Combine like terms: -22.450835174 + -0.2 = -22.650835174 x = -22.650835174 Simplifying x = -22.650835174Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.250835174, -22.650835174}Solution
x = {22.250835174, -22.650835174}
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