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Simplifying 60x2 + 54x + 8 = 0 Reorder the terms: 8 + 54x + 60x2 = 0 Solving 8 + 54x + 60x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(4 + 27x + 30x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + 27x + 30x2)' equal to zero and attempt to solve: Simplifying 4 + 27x + 30x2 = 0 Solving 4 + 27x + 30x2 = 0 Begin completing the square. Divide all terms by 30 the coefficient of the squared term: Divide each side by '30'. 0.1333333333 + 0.9x + x2 = 0.0 Move the constant term to the right: Add '-0.1333333333' to each side of the equation. 0.1333333333 + 0.9x + -0.1333333333 + x2 = 0.0 + -0.1333333333 Reorder the terms: 0.1333333333 + -0.1333333333 + 0.9x + x2 = 0.0 + -0.1333333333 Combine like terms: 0.1333333333 + -0.1333333333 = 0.0000000000 0.0000000000 + 0.9x + x2 = 0.0 + -0.1333333333 0.9x + x2 = 0.0 + -0.1333333333 Combine like terms: 0.0 + -0.1333333333 = -0.1333333333 0.9x + x2 = -0.1333333333 The x term is 0.9x. Take half its coefficient (0.45). Square it (0.2025) and add it to both sides. Add '0.2025' to each side of the equation. 0.9x + 0.2025 + x2 = -0.1333333333 + 0.2025 Reorder the terms: 0.2025 + 0.9x + x2 = -0.1333333333 + 0.2025 Combine like terms: -0.1333333333 + 0.2025 = 0.0691666667 0.2025 + 0.9x + x2 = 0.0691666667 Factor a perfect square on the left side: (x + 0.45)(x + 0.45) = 0.0691666667 Calculate the square root of the right side: 0.262995564 Break this problem into two subproblems by setting (x + 0.45) equal to 0.262995564 and -0.262995564.Subproblem 1
x + 0.45 = 0.262995564 Simplifying x + 0.45 = 0.262995564 Reorder the terms: 0.45 + x = 0.262995564 Solving 0.45 + x = 0.262995564 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.45' to each side of the equation. 0.45 + -0.45 + x = 0.262995564 + -0.45 Combine like terms: 0.45 + -0.45 = 0.00 0.00 + x = 0.262995564 + -0.45 x = 0.262995564 + -0.45 Combine like terms: 0.262995564 + -0.45 = -0.187004436 x = -0.187004436 Simplifying x = -0.187004436Subproblem 2
x + 0.45 = -0.262995564 Simplifying x + 0.45 = -0.262995564 Reorder the terms: 0.45 + x = -0.262995564 Solving 0.45 + x = -0.262995564 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.45' to each side of the equation. 0.45 + -0.45 + x = -0.262995564 + -0.45 Combine like terms: 0.45 + -0.45 = 0.00 0.00 + x = -0.262995564 + -0.45 x = -0.262995564 + -0.45 Combine like terms: -0.262995564 + -0.45 = -0.712995564 x = -0.712995564 Simplifying x = -0.712995564Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.187004436, -0.712995564}Solution
x = {-0.187004436, -0.712995564}
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