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Simplifying 10x2 + 50x + -625 = 0 Reorder the terms: -625 + 50x + 10x2 = 0 Solving -625 + 50x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-125 + 10x + 2x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-125 + 10x + 2x2)' equal to zero and attempt to solve: Simplifying -125 + 10x + 2x2 = 0 Solving -125 + 10x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -62.5 + 5x + x2 = 0 Move the constant term to the right: Add '62.5' to each side of the equation. -62.5 + 5x + 62.5 + x2 = 0 + 62.5 Reorder the terms: -62.5 + 62.5 + 5x + x2 = 0 + 62.5 Combine like terms: -62.5 + 62.5 = 0.0 0.0 + 5x + x2 = 0 + 62.5 5x + x2 = 0 + 62.5 Combine like terms: 0 + 62.5 = 62.5 5x + x2 = 62.5 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 62.5 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 62.5 + 6.25 Combine like terms: 62.5 + 6.25 = 68.75 6.25 + 5x + x2 = 68.75 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 68.75 Calculate the square root of the right side: 8.291561976 Break this problem into two subproblems by setting (x + 2.5) equal to 8.291561976 and -8.291561976.Subproblem 1
x + 2.5 = 8.291561976 Simplifying x + 2.5 = 8.291561976 Reorder the terms: 2.5 + x = 8.291561976 Solving 2.5 + x = 8.291561976 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 8.291561976 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 8.291561976 + -2.5 x = 8.291561976 + -2.5 Combine like terms: 8.291561976 + -2.5 = 5.791561976 x = 5.791561976 Simplifying x = 5.791561976Subproblem 2
x + 2.5 = -8.291561976 Simplifying x + 2.5 = -8.291561976 Reorder the terms: 2.5 + x = -8.291561976 Solving 2.5 + x = -8.291561976 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -8.291561976 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -8.291561976 + -2.5 x = -8.291561976 + -2.5 Combine like terms: -8.291561976 + -2.5 = -10.791561976 x = -10.791561976 Simplifying x = -10.791561976Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.791561976, -10.791561976}Solution
x = {5.791561976, -10.791561976}
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