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Simplifying 25x2 + 625x + 5 = 0 Reorder the terms: 5 + 625x + 25x2 = 0 Solving 5 + 625x + 25x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(1 + 125x + 5x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(1 + 125x + 5x2)' equal to zero and attempt to solve: Simplifying 1 + 125x + 5x2 = 0 Solving 1 + 125x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.2 + 25x + x2 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + 25x + -0.2 + x2 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + 25x + x2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + 25x + x2 = 0 + -0.2 25x + x2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 25x + x2 = -0.2 The x term is 25x. Take half its coefficient (12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. 25x + 156.25 + x2 = -0.2 + 156.25 Reorder the terms: 156.25 + 25x + x2 = -0.2 + 156.25 Combine like terms: -0.2 + 156.25 = 156.05 156.25 + 25x + x2 = 156.05 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 156.05 Calculate the square root of the right side: 12.491997438 Break this problem into two subproblems by setting (x + 12.5) equal to 12.491997438 and -12.491997438.Subproblem 1
x + 12.5 = 12.491997438 Simplifying x + 12.5 = 12.491997438 Reorder the terms: 12.5 + x = 12.491997438 Solving 12.5 + x = 12.491997438 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = 12.491997438 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 12.491997438 + -12.5 x = 12.491997438 + -12.5 Combine like terms: 12.491997438 + -12.5 = -0.008002562 x = -0.008002562 Simplifying x = -0.008002562Subproblem 2
x + 12.5 = -12.491997438 Simplifying x + 12.5 = -12.491997438 Reorder the terms: 12.5 + x = -12.491997438 Solving 12.5 + x = -12.491997438 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = -12.491997438 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -12.491997438 + -12.5 x = -12.491997438 + -12.5 Combine like terms: -12.491997438 + -12.5 = -24.991997438 x = -24.991997438 Simplifying x = -24.991997438Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.008002562, -24.991997438}Solution
x = {-0.008002562, -24.991997438}
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