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Simplifying (3x + -1)(x + 3.464101615) = 0 Reorder the terms: (-1 + 3x)(x + 3.464101615) = 0 Reorder the terms: (-1 + 3x)(3.464101615 + x) = 0 Multiply (-1 + 3x) * (3.464101615 + x) (-1(3.464101615 + x) + 3x * (3.464101615 + x)) = 0 ((3.464101615 * -1 + x * -1) + 3x * (3.464101615 + x)) = 0 ((-3.464101615 + -1x) + 3x * (3.464101615 + x)) = 0 (-3.464101615 + -1x + (3.464101615 * 3x + x * 3x)) = 0 (-3.464101615 + -1x + (10.39230485x + 3x2)) = 0 Combine like terms: -1x + 10.39230485x = 9.39230485x (-3.464101615 + 9.39230485x + 3x2) = 0 Solving -3.464101615 + 9.39230485x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1.154700538 + 3.130768283x + x2 = 0 Move the constant term to the right: Add '1.154700538' to each side of the equation. -1.154700538 + 3.130768283x + 1.154700538 + x2 = 0 + 1.154700538 Reorder the terms: -1.154700538 + 1.154700538 + 3.130768283x + x2 = 0 + 1.154700538 Combine like terms: -1.154700538 + 1.154700538 = 0.000000000 0.000000000 + 3.130768283x + x2 = 0 + 1.154700538 3.130768283x + x2 = 0 + 1.154700538 Combine like terms: 0 + 1.154700538 = 1.154700538 3.130768283x + x2 = 1.154700538 The x term is 3.130768283x. Take half its coefficient (1.565384142). Square it (2.450427512) and add it to both sides. Add '2.450427512' to each side of the equation. 3.130768283x + 2.450427512 + x2 = 1.154700538 + 2.450427512 Reorder the terms: 2.450427512 + 3.130768283x + x2 = 1.154700538 + 2.450427512 Combine like terms: 1.154700538 + 2.450427512 = 3.60512805 2.450427512 + 3.130768283x + x2 = 3.60512805 Factor a perfect square on the left side: (x + 1.565384142)(x + 1.565384142) = 3.60512805 Calculate the square root of the right side: 1.898717475 Break this problem into two subproblems by setting (x + 1.565384142) equal to 1.898717475 and -1.898717475.Subproblem 1
x + 1.565384142 = 1.898717475 Simplifying x + 1.565384142 = 1.898717475 Reorder the terms: 1.565384142 + x = 1.898717475 Solving 1.565384142 + x = 1.898717475 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.565384142' to each side of the equation. 1.565384142 + -1.565384142 + x = 1.898717475 + -1.565384142 Combine like terms: 1.565384142 + -1.565384142 = 0.000000000 0.000000000 + x = 1.898717475 + -1.565384142 x = 1.898717475 + -1.565384142 Combine like terms: 1.898717475 + -1.565384142 = 0.333333333 x = 0.333333333 Simplifying x = 0.333333333Subproblem 2
x + 1.565384142 = -1.898717475 Simplifying x + 1.565384142 = -1.898717475 Reorder the terms: 1.565384142 + x = -1.898717475 Solving 1.565384142 + x = -1.898717475 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.565384142' to each side of the equation. 1.565384142 + -1.565384142 + x = -1.898717475 + -1.565384142 Combine like terms: 1.565384142 + -1.565384142 = 0.000000000 0.000000000 + x = -1.898717475 + -1.565384142 x = -1.898717475 + -1.565384142 Combine like terms: -1.898717475 + -1.565384142 = -3.464101617 x = -3.464101617 Simplifying x = -3.464101617Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.333333333, -3.464101617}
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