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Simplifying 54x2 + 54x + 10 = 0 Reorder the terms: 10 + 54x + 54x2 = 0 Solving 10 + 54x + 54x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + 27x + 27x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + 27x + 27x2)' equal to zero and attempt to solve: Simplifying 5 + 27x + 27x2 = 0 Solving 5 + 27x + 27x2 = 0 Begin completing the square. Divide all terms by 27 the coefficient of the squared term: Divide each side by '27'. 0.1851851852 + x + x2 = 0 Move the constant term to the right: Add '-0.1851851852' to each side of the equation. 0.1851851852 + x + -0.1851851852 + x2 = 0 + -0.1851851852 Reorder the terms: 0.1851851852 + -0.1851851852 + x + x2 = 0 + -0.1851851852 Combine like terms: 0.1851851852 + -0.1851851852 = 0.0000000000 0.0000000000 + x + x2 = 0 + -0.1851851852 x + x2 = 0 + -0.1851851852 Combine like terms: 0 + -0.1851851852 = -0.1851851852 x + x2 = -0.1851851852 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 = -0.1851851852 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = -0.1851851852 + 0.25 Combine like terms: -0.1851851852 + 0.25 = 0.0648148148 1.25 + x2 = 0.0648148148 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.0648148148 Calculate the square root of the right side: 0.254587539 Break this problem into two subproblems by setting (x + 0.5) equal to 0.254587539 and -0.254587539.Subproblem 1
x + 0.5 = 0.254587539 Simplifying x + 0.5 = 0.254587539 Reorder the terms: 0.5 + x = 0.254587539 Solving 0.5 + x = 0.254587539 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 = 0.254587539 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.254587539 + -0.5 x = 0.254587539 + -0.5 Combine like terms: 0.254587539 + -0.5 = -0.245412461 x = -0.245412461 Simplifying x = -0.245412461Subproblem 2
x + 0.5 = -0.254587539 Simplifying x + 0.5 = -0.254587539 Reorder the terms: 0.5 + x = -0.254587539 Solving 0.5 + x = -0.254587539 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 = -0.254587539 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.254587539 + -0.5 x = -0.254587539 + -0.5 Combine like terms: -0.254587539 + -0.5 = -0.754587539 x = -0.754587539 Simplifying x = -0.754587539Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.245412461, -0.754587539}Solution
x = {-0.245412461, -0.754587539}
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