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Simplifying 55x2 + 55x + -100 = 0 Reorder the terms: -100 + 55x + 55x2 = 0 Solving -100 + 55x + 55x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-20 + 11x + 11x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-20 + 11x + 11x2)' equal to zero and attempt to solve: Simplifying -20 + 11x + 11x2 = 0 Solving -20 + 11x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -1.818181818 + x + x2 = 0 Move the constant term to the right: Add '1.818181818' to each side of the equation. -1.818181818 + x + 1.818181818 + x2 = 0 + 1.818181818 Reorder the terms: -1.818181818 + 1.818181818 + x + x2 = 0 + 1.818181818 Combine like terms: -1.818181818 + 1.818181818 = 0.000000000 0.000000000 + x + x2 = 0 + 1.818181818 x + x2 = 0 + 1.818181818 Combine like terms: 0 + 1.818181818 = 1.818181818 x + x2 = 1.818181818 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. + 0.25 + x2 = 1.818181818 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 1.818181818 + 0.25 Combine like terms: 1.818181818 + 0.25 = 2.068181818 1.25 + x2 = 2.068181818 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 2.068181818 Calculate the square root of the right side: 1.438117456 Break this problem into two subproblems by setting (x + 0.5) equal to 1.438117456 and -1.438117456.Subproblem 1
x + 0.5 = 1.438117456 Simplifying x + 0.5 = 1.438117456 Reorder the terms: 0.5 + x = 1.438117456 Solving 0.5 + x = 1.438117456 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 = 1.438117456 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.438117456 + -0.5 x = 1.438117456 + -0.5 Combine like terms: 1.438117456 + -0.5 = 0.938117456 x = 0.938117456 Simplifying x = 0.938117456Subproblem 2
x + 0.5 = -1.438117456 Simplifying x + 0.5 = -1.438117456 Reorder the terms: 0.5 + x = -1.438117456 Solving 0.5 + x = -1.438117456 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 = -1.438117456 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.438117456 + -0.5 x = -1.438117456 + -0.5 Combine like terms: -1.438117456 + -0.5 = -1.938117456 x = -1.938117456 Simplifying x = -1.938117456Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.938117456, -1.938117456}Solution
x = {0.938117456, -1.938117456}
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