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Simplifying 40x2 + -400x + 500 = 0 Reorder the terms: 500 + -400x + 40x2 = 0 Solving 500 + -400x + 40x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '20'. 20(25 + -20x + 2x2) = 0 Ignore the factor 20.Subproblem 1
Set the factor '(25 + -20x + 2x2)' equal to zero and attempt to solve: Simplifying 25 + -20x + 2x2 = 0 Solving 25 + -20x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 12.5 + -10x + x2 = 0 Move the constant term to the right: Add '-12.5' to each side of the equation. 12.5 + -10x + -12.5 + x2 = 0 + -12.5 Reorder the terms: 12.5 + -12.5 + -10x + x2 = 0 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + -10x + x2 = 0 + -12.5 -10x + x2 = 0 + -12.5 Combine like terms: 0 + -12.5 = -12.5 -10x + x2 = -12.5 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -12.5 + 25 Reorder the terms: 25 + -10x + x2 = -12.5 + 25 Combine like terms: -12.5 + 25 = 12.5 25 + -10x + x2 = 12.5 Factor a perfect square on the left side: (x + -5)(x + -5) = 12.5 Calculate the square root of the right side: 3.535533906 Break this problem into two subproblems by setting (x + -5) equal to 3.535533906 and -3.535533906.Subproblem 1
x + -5 = 3.535533906 Simplifying x + -5 = 3.535533906 Reorder the terms: -5 + x = 3.535533906 Solving -5 + x = 3.535533906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 3.535533906 + 5 Combine like terms: -5 + 5 = 0 0 + x = 3.535533906 + 5 x = 3.535533906 + 5 Combine like terms: 3.535533906 + 5 = 8.535533906 x = 8.535533906 Simplifying x = 8.535533906Subproblem 2
x + -5 = -3.535533906 Simplifying x + -5 = -3.535533906 Reorder the terms: -5 + x = -3.535533906 Solving -5 + x = -3.535533906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -3.535533906 + 5 Combine like terms: -5 + 5 = 0 0 + x = -3.535533906 + 5 x = -3.535533906 + 5 Combine like terms: -3.535533906 + 5 = 1.464466094 x = 1.464466094 Simplifying x = 1.464466094Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.535533906, 1.464466094}Solution
x = {8.535533906, 1.464466094}
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