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Simplifying 100x2 + 50x + 2 = 0 Reorder the terms: 2 + 50x + 100x2 = 0 Solving 2 + 50x + 100x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(1 + 25x + 50x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + 25x + 50x2)' equal to zero and attempt to solve: Simplifying 1 + 25x + 50x2 = 0 Solving 1 + 25x + 50x2 = 0 Begin completing the square. Divide all terms by 50 the coefficient of the squared term: Divide each side by '50'. 0.02 + 0.5x + x2 = 0.0 Move the constant term to the right: Add '-0.02' to each side of the equation. 0.02 + 0.5x + -0.02 + x2 = 0.0 + -0.02 Reorder the terms: 0.02 + -0.02 + 0.5x + x2 = 0.0 + -0.02 Combine like terms: 0.02 + -0.02 = 0.00 0.00 + 0.5x + x2 = 0.0 + -0.02 0.5x + x2 = 0.0 + -0.02 Combine like terms: 0.0 + -0.02 = -0.02 0.5x + x2 = -0.02 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = -0.02 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = -0.02 + 0.0625 Combine like terms: -0.02 + 0.0625 = 0.0425 0.0625 + 0.5x + x2 = 0.0425 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 0.0425 Calculate the square root of the right side: 0.206155281 Break this problem into two subproblems by setting (x + 0.25) equal to 0.206155281 and -0.206155281.Subproblem 1
x + 0.25 = 0.206155281 Simplifying x + 0.25 = 0.206155281 Reorder the terms: 0.25 + x = 0.206155281 Solving 0.25 + x = 0.206155281 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 0.206155281 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 0.206155281 + -0.25 x = 0.206155281 + -0.25 Combine like terms: 0.206155281 + -0.25 = -0.043844719 x = -0.043844719 Simplifying x = -0.043844719Subproblem 2
x + 0.25 = -0.206155281 Simplifying x + 0.25 = -0.206155281 Reorder the terms: 0.25 + x = -0.206155281 Solving 0.25 + x = -0.206155281 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -0.206155281 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -0.206155281 + -0.25 x = -0.206155281 + -0.25 Combine like terms: -0.206155281 + -0.25 = -0.456155281 x = -0.456155281 Simplifying x = -0.456155281Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.043844719, -0.456155281}Solution
x = {-0.043844719, -0.456155281}
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