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Simplifying 50x2 + 20x = 13400 Reorder the terms: 20x + 50x2 = 13400 Solving 20x + 50x2 = 13400 Solving for variable 'x'. Reorder the terms: -13400 + 20x + 50x2 = 13400 + -13400 Combine like terms: 13400 + -13400 = 0 -13400 + 20x + 50x2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(-1340 + 2x + 5x2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-1340 + 2x + 5x2)' equal to zero and attempt to solve: Simplifying -1340 + 2x + 5x2 = 0 Solving -1340 + 2x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -268 + 0.4x + x2 = 0 Move the constant term to the right: Add '268' to each side of the equation. -268 + 0.4x + 268 + x2 = 0 + 268 Reorder the terms: -268 + 268 + 0.4x + x2 = 0 + 268 Combine like terms: -268 + 268 = 0 0 + 0.4x + x2 = 0 + 268 0.4x + x2 = 0 + 268 Combine like terms: 0 + 268 = 268 0.4x + x2 = 268 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 = 268 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 268 + 0.04 Combine like terms: 268 + 0.04 = 268.04 0.04 + 0.4x + x2 = 268.04 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 268.04 Calculate the square root of the right side: 16.371927193 Break this problem into two subproblems by setting (x + 0.2) equal to 16.371927193 and -16.371927193.Subproblem 1
x + 0.2 = 16.371927193 Simplifying x + 0.2 = 16.371927193 Reorder the terms: 0.2 + x = 16.371927193 Solving 0.2 + x = 16.371927193 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 = 16.371927193 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 16.371927193 + -0.2 x = 16.371927193 + -0.2 Combine like terms: 16.371927193 + -0.2 = 16.171927193 x = 16.171927193 Simplifying x = 16.171927193Subproblem 2
x + 0.2 = -16.371927193 Simplifying x + 0.2 = -16.371927193 Reorder the terms: 0.2 + x = -16.371927193 Solving 0.2 + x = -16.371927193 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 = -16.371927193 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -16.371927193 + -0.2 x = -16.371927193 + -0.2 Combine like terms: -16.371927193 + -0.2 = -16.571927193 x = -16.571927193 Simplifying x = -16.571927193Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.171927193, -16.571927193}Solution
x = {16.171927193, -16.571927193}
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