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Simplifying 18x2 + 40x + 18 = 0 Reorder the terms: 18 + 40x + 18x2 = 0 Solving 18 + 40x + 18x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(9 + 20x + 9x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(9 + 20x + 9x2)' equal to zero and attempt to solve: Simplifying 9 + 20x + 9x2 = 0 Solving 9 + 20x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 1 + 2.222222222x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 2.222222222x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 2.222222222x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2.222222222x + x2 = 0 + -1 2.222222222x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 2.222222222x + x2 = -1 The x term is 2.222222222x. Take half its coefficient (1.111111111). Square it (1.234567901) and add it to both sides. Add '1.234567901' to each side of the equation. 2.222222222x + 1.234567901 + x2 = -1 + 1.234567901 Reorder the terms: 1.234567901 + 2.222222222x + x2 = -1 + 1.234567901 Combine like terms: -1 + 1.234567901 = 0.234567901 1.234567901 + 2.222222222x + x2 = 0.234567901 Factor a perfect square on the left side: (x + 1.111111111)(x + 1.111111111) = 0.234567901 Calculate the square root of the right side: 0.484322105 Break this problem into two subproblems by setting (x + 1.111111111) equal to 0.484322105 and -0.484322105.Subproblem 1
x + 1.111111111 = 0.484322105 Simplifying x + 1.111111111 = 0.484322105 Reorder the terms: 1.111111111 + x = 0.484322105 Solving 1.111111111 + x = 0.484322105 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.111111111' to each side of the equation. 1.111111111 + -1.111111111 + x = 0.484322105 + -1.111111111 Combine like terms: 1.111111111 + -1.111111111 = 0.000000000 0.000000000 + x = 0.484322105 + -1.111111111 x = 0.484322105 + -1.111111111 Combine like terms: 0.484322105 + -1.111111111 = -0.626789006 x = -0.626789006 Simplifying x = -0.626789006Subproblem 2
x + 1.111111111 = -0.484322105 Simplifying x + 1.111111111 = -0.484322105 Reorder the terms: 1.111111111 + x = -0.484322105 Solving 1.111111111 + x = -0.484322105 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.111111111' to each side of the equation. 1.111111111 + -1.111111111 + x = -0.484322105 + -1.111111111 Combine like terms: 1.111111111 + -1.111111111 = 0.000000000 0.000000000 + x = -0.484322105 + -1.111111111 x = -0.484322105 + -1.111111111 Combine like terms: -0.484322105 + -1.111111111 = -1.595433216 x = -1.595433216 Simplifying x = -1.595433216Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.626789006, -1.595433216}Solution
x = {-0.626789006, -1.595433216}
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