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Simplifying 100x2 + 5x + 5 = 0 Reorder the terms: 5 + 5x + 100x2 = 0 Solving 5 + 5x + 100x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(1 + x + 20x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(1 + x + 20x2)' equal to zero and attempt to solve: Simplifying 1 + x + 20x2 = 0 Solving 1 + x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. 0.05 + 0.05x + x2 = 0.0 Move the constant term to the right: Add '-0.05' to each side of the equation. 0.05 + 0.05x + -0.05 + x2 = 0.0 + -0.05 Reorder the terms: 0.05 + -0.05 + 0.05x + x2 = 0.0 + -0.05 Combine like terms: 0.05 + -0.05 = 0.00 0.00 + 0.05x + x2 = 0.0 + -0.05 0.05x + x2 = 0.0 + -0.05 Combine like terms: 0.0 + -0.05 = -0.05 0.05x + x2 = -0.05 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.05x + 0.25 + x2 = -0.05 + 0.25 Reorder the terms: 0.25 + 0.05x + x2 = -0.05 + 0.25 Combine like terms: -0.05 + 0.25 = 0.2 0.25 + 0.05x + x2 = 0.2 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.2 Calculate the square root of the right side: 0.447213596 Break this problem into two subproblems by setting (x + 0.5) equal to 0.447213596 and -0.447213596.Subproblem 1
x + 0.5 = 0.447213596 Simplifying x + 0.5 = 0.447213596 Reorder the terms: 0.5 + x = 0.447213596 Solving 0.5 + x = 0.447213596 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.447213596 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.447213596 + -0.5 x = 0.447213596 + -0.5 Combine like terms: 0.447213596 + -0.5 = -0.052786404 x = -0.052786404 Simplifying x = -0.052786404Subproblem 2
x + 0.5 = -0.447213596 Simplifying x + 0.5 = -0.447213596 Reorder the terms: 0.5 + x = -0.447213596 Solving 0.5 + x = -0.447213596 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.447213596 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.447213596 + -0.5 x = -0.447213596 + -0.5 Combine like terms: -0.447213596 + -0.5 = -0.947213596 x = -0.947213596 Simplifying x = -0.947213596Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.052786404, -0.947213596}Solution
x = {-0.052786404, -0.947213596}
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