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Simplifying 18x2 + 6x = 5 Reorder the terms: 6x + 18x2 = 5 Solving 6x + 18x2 = 5 Solving for variable 'x'. Reorder the terms: -5 + 6x + 18x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 6x + 18x2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -0.2777777778 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '0.2777777778' to each side of the equation. -0.2777777778 + 0.3333333333x + 0.2777777778 + x2 = 0 + 0.2777777778 Reorder the terms: -0.2777777778 + 0.2777777778 + 0.3333333333x + x2 = 0 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + 0.3333333333x + x2 = 0 + 0.2777777778 0.3333333333x + x2 = 0 + 0.2777777778 Combine like terms: 0 + 0.2777777778 = 0.2777777778 0.3333333333x + x2 = 0.2777777778 The x term is 0.3333333333x. Take half its coefficient (0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. 0.3333333333x + 0.02777777779 + x2 = 0.2777777778 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333x + x2 = 0.2777777778 + 0.02777777779 Combine like terms: 0.2777777778 + 0.02777777779 = 0.30555555559 0.02777777779 + 0.3333333333x + x2 = 0.30555555559 Factor a perfect square on the left side: (x + 0.1666666667)(x + 0.1666666667) = 0.30555555559 Calculate the square root of the right side: 0.552770798 Break this problem into two subproblems by setting (x + 0.1666666667) equal to 0.552770798 and -0.552770798.Subproblem 1
x + 0.1666666667 = 0.552770798 Simplifying x + 0.1666666667 = 0.552770798 Reorder the terms: 0.1666666667 + x = 0.552770798 Solving 0.1666666667 + x = 0.552770798 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = 0.552770798 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = 0.552770798 + -0.1666666667 x = 0.552770798 + -0.1666666667 Combine like terms: 0.552770798 + -0.1666666667 = 0.3861041313 x = 0.3861041313 Simplifying x = 0.3861041313Subproblem 2
x + 0.1666666667 = -0.552770798 Simplifying x + 0.1666666667 = -0.552770798 Reorder the terms: 0.1666666667 + x = -0.552770798 Solving 0.1666666667 + x = -0.552770798 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = -0.552770798 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = -0.552770798 + -0.1666666667 x = -0.552770798 + -0.1666666667 Combine like terms: -0.552770798 + -0.1666666667 = -0.7194374647 x = -0.7194374647 Simplifying x = -0.7194374647Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3861041313, -0.7194374647}
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