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Simplifying 18x2 + 12x + 1 = 0 Reorder the terms: 1 + 12x + 18x2 = 0 Solving 1 + 12x + 18x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. 0.05555555556 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '-0.05555555556' to each side of the equation. 0.05555555556 + 0.6666666667x + -0.05555555556 + x2 = 0 + -0.05555555556 Reorder the terms: 0.05555555556 + -0.05555555556 + 0.6666666667x + x2 = 0 + -0.05555555556 Combine like terms: 0.05555555556 + -0.05555555556 = 0.00000000000 0.00000000000 + 0.6666666667x + x2 = 0 + -0.05555555556 0.6666666667x + x2 = 0 + -0.05555555556 Combine like terms: 0 + -0.05555555556 = -0.05555555556 0.6666666667x + x2 = -0.05555555556 The x term is 0.6666666667x. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667x + 0.1111111112 + x2 = -0.05555555556 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = -0.05555555556 + 0.1111111112 Combine like terms: -0.05555555556 + 0.1111111112 = 0.05555555564 0.1111111112 + 0.6666666667x + x2 = 0.05555555564 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 0.05555555564 Calculate the square root of the right side: 0.235702261 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 0.235702261 and -0.235702261.Subproblem 1
x + 0.3333333334 = 0.235702261 Simplifying x + 0.3333333334 = 0.235702261 Reorder the terms: 0.3333333334 + x = 0.235702261 Solving 0.3333333334 + x = 0.235702261 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = 0.235702261 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 0.235702261 + -0.3333333334 x = 0.235702261 + -0.3333333334 Combine like terms: 0.235702261 + -0.3333333334 = -0.0976310724 x = -0.0976310724 Simplifying x = -0.0976310724Subproblem 2
x + 0.3333333334 = -0.235702261 Simplifying x + 0.3333333334 = -0.235702261 Reorder the terms: 0.3333333334 + x = -0.235702261 Solving 0.3333333334 + x = -0.235702261 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = -0.235702261 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -0.235702261 + -0.3333333334 x = -0.235702261 + -0.3333333334 Combine like terms: -0.235702261 + -0.3333333334 = -0.5690355944 x = -0.5690355944 Simplifying x = -0.5690355944Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.0976310724, -0.5690355944}
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