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Simplifying 5x2 + 20x = 125 Reorder the terms: 20x + 5x2 = 125 Solving 20x + 5x2 = 125 Solving for variable 'x'. Reorder the terms: -125 + 20x + 5x2 = 125 + -125 Combine like terms: 125 + -125 = 0 -125 + 20x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-25 + 4x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-25 + 4x + x2)' equal to zero and attempt to solve: Simplifying -25 + 4x + x2 = 0 Solving -25 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + 4x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + 4x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 4x + x2 = 0 + 25 4x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 4x + x2 = 25 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 25 + 4 Reorder the terms: 4 + 4x + x2 = 25 + 4 Combine like terms: 25 + 4 = 29 4 + 4x + x2 = 29 Factor a perfect square on the left side: (x + 2)(x + 2) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (x + 2) equal to 5.385164807 and -5.385164807.Subproblem 1
x + 2 = 5.385164807 Simplifying x + 2 = 5.385164807 Reorder the terms: 2 + x = 5.385164807 Solving 2 + x = 5.385164807 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 5.385164807 + -2 Combine like terms: 2 + -2 = 0 0 + x = 5.385164807 + -2 x = 5.385164807 + -2 Combine like terms: 5.385164807 + -2 = 3.385164807 x = 3.385164807 Simplifying x = 3.385164807Subproblem 2
x + 2 = -5.385164807 Simplifying x + 2 = -5.385164807 Reorder the terms: 2 + x = -5.385164807 Solving 2 + x = -5.385164807 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -5.385164807 + -2 Combine like terms: 2 + -2 = 0 0 + x = -5.385164807 + -2 x = -5.385164807 + -2 Combine like terms: -5.385164807 + -2 = -7.385164807 x = -7.385164807 Simplifying x = -7.385164807Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.385164807, -7.385164807}Solution
x = {3.385164807, -7.385164807}
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