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Simplifying 18x2 + 22x + 2 = 0 Reorder the terms: 2 + 22x + 18x2 = 0 Solving 2 + 22x + 18x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(1 + 11x + 9x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + 11x + 9x2)' equal to zero and attempt to solve: Simplifying 1 + 11x + 9x2 = 0 Solving 1 + 11x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.1111111111 + 1.222222222x + x2 = 0 Move the constant term to the right: Add '-0.1111111111' to each side of the equation. 0.1111111111 + 1.222222222x + -0.1111111111 + x2 = 0 + -0.1111111111 Reorder the terms: 0.1111111111 + -0.1111111111 + 1.222222222x + x2 = 0 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + 1.222222222x + x2 = 0 + -0.1111111111 1.222222222x + x2 = 0 + -0.1111111111 Combine like terms: 0 + -0.1111111111 = -0.1111111111 1.222222222x + x2 = -0.1111111111 The x term is 1.222222222x. Take half its coefficient (0.611111111). Square it (0.3734567900) and add it to both sides. Add '0.3734567900' to each side of the equation. 1.222222222x + 0.3734567900 + x2 = -0.1111111111 + 0.3734567900 Reorder the terms: 0.3734567900 + 1.222222222x + x2 = -0.1111111111 + 0.3734567900 Combine like terms: -0.1111111111 + 0.3734567900 = 0.2623456789 0.3734567900 + 1.222222222x + x2 = 0.2623456789 Factor a perfect square on the left side: (x + 0.611111111)(x + 0.611111111) = 0.2623456789 Calculate the square root of the right side: 0.512196914 Break this problem into two subproblems by setting (x + 0.611111111) equal to 0.512196914 and -0.512196914.Subproblem 1
x + 0.611111111 = 0.512196914 Simplifying x + 0.611111111 = 0.512196914 Reorder the terms: 0.611111111 + x = 0.512196914 Solving 0.611111111 + x = 0.512196914 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.611111111' to each side of the equation. 0.611111111 + -0.611111111 + x = 0.512196914 + -0.611111111 Combine like terms: 0.611111111 + -0.611111111 = 0.000000000 0.000000000 + x = 0.512196914 + -0.611111111 x = 0.512196914 + -0.611111111 Combine like terms: 0.512196914 + -0.611111111 = -0.098914197 x = -0.098914197 Simplifying x = -0.098914197Subproblem 2
x + 0.611111111 = -0.512196914 Simplifying x + 0.611111111 = -0.512196914 Reorder the terms: 0.611111111 + x = -0.512196914 Solving 0.611111111 + x = -0.512196914 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.611111111' to each side of the equation. 0.611111111 + -0.611111111 + x = -0.512196914 + -0.611111111 Combine like terms: 0.611111111 + -0.611111111 = 0.000000000 0.000000000 + x = -0.512196914 + -0.611111111 x = -0.512196914 + -0.611111111 Combine like terms: -0.512196914 + -0.611111111 = -1.123308025 x = -1.123308025 Simplifying x = -1.123308025Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.098914197, -1.123308025}Solution
x = {-0.098914197, -1.123308025}
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