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Simplifying 200x2 + -65x + -10 = 0 Reorder the terms: -10 + -65x + 200x2 = 0 Solving -10 + -65x + 200x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-2 + -13x + 40x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-2 + -13x + 40x2)' equal to zero and attempt to solve: Simplifying -2 + -13x + 40x2 = 0 Solving -2 + -13x + 40x2 = 0 Begin completing the square. Divide all terms by 40 the coefficient of the squared term: Divide each side by '40'. -0.05 + -0.325x + x2 = 0.0 Move the constant term to the right: Add '0.05' to each side of the equation. -0.05 + -0.325x + 0.05 + x2 = 0.0 + 0.05 Reorder the terms: -0.05 + 0.05 + -0.325x + x2 = 0.0 + 0.05 Combine like terms: -0.05 + 0.05 = 0.00 0.00 + -0.325x + x2 = 0.0 + 0.05 -0.325x + x2 = 0.0 + 0.05 Combine like terms: 0.0 + 0.05 = 0.05 -0.325x + x2 = 0.05 The x term is -0.325x. Take half its coefficient (-0.1625). Square it (0.02640625) and add it to both sides. Add '0.02640625' to each side of the equation. -0.325x + 0.02640625 + x2 = 0.05 + 0.02640625 Reorder the terms: 0.02640625 + -0.325x + x2 = 0.05 + 0.02640625 Combine like terms: 0.05 + 0.02640625 = 0.07640625 0.02640625 + -0.325x + x2 = 0.07640625 Factor a perfect square on the left side: (x + -0.1625)(x + -0.1625) = 0.07640625 Calculate the square root of the right side: 0.276416805 Break this problem into two subproblems by setting (x + -0.1625) equal to 0.276416805 and -0.276416805.Subproblem 1
x + -0.1625 = 0.276416805 Simplifying x + -0.1625 = 0.276416805 Reorder the terms: -0.1625 + x = 0.276416805 Solving -0.1625 + x = 0.276416805 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1625' to each side of the equation. -0.1625 + 0.1625 + x = 0.276416805 + 0.1625 Combine like terms: -0.1625 + 0.1625 = 0.0000 0.0000 + x = 0.276416805 + 0.1625 x = 0.276416805 + 0.1625 Combine like terms: 0.276416805 + 0.1625 = 0.438916805 x = 0.438916805 Simplifying x = 0.438916805Subproblem 2
x + -0.1625 = -0.276416805 Simplifying x + -0.1625 = -0.276416805 Reorder the terms: -0.1625 + x = -0.276416805 Solving -0.1625 + x = -0.276416805 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1625' to each side of the equation. -0.1625 + 0.1625 + x = -0.276416805 + 0.1625 Combine like terms: -0.1625 + 0.1625 = 0.0000 0.0000 + x = -0.276416805 + 0.1625 x = -0.276416805 + 0.1625 Combine like terms: -0.276416805 + 0.1625 = -0.113916805 x = -0.113916805 Simplifying x = -0.113916805Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.438916805, -0.113916805}Solution
x = {0.438916805, -0.113916805}
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