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Simplifying x(3x + 1) = 6 Reorder the terms: x(1 + 3x) = 6 (1 * x + 3x * x) = 6 (1x + 3x2) = 6 Solving 1x + 3x2 = 6 Solving for variable 'x'. Reorder the terms: -6 + 1x + 3x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + 1x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 0.3333333333x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 0.3333333333x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 0.3333333333x + x2 = 0 + 2 0.3333333333x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 0.3333333333x + x2 = 2 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 = 2 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333x + x2 = 2 + 0.02777777779 Combine like terms: 2 + 0.02777777779 = 2.02777777779 0.02777777779 + 0.3333333333x + x2 = 2.02777777779 Factor a perfect square on the left side: (x + 0.1666666667)(x + 0.1666666667) = 2.02777777779 Calculate the square root of the right side: 1.424000624 Break this problem into two subproblems by setting (x + 0.1666666667) equal to 1.424000624 and -1.424000624.Subproblem 1
x + 0.1666666667 = 1.424000624 Simplifying x + 0.1666666667 = 1.424000624 Reorder the terms: 0.1666666667 + x = 1.424000624 Solving 0.1666666667 + x = 1.424000624 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 = 1.424000624 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = 1.424000624 + -0.1666666667 x = 1.424000624 + -0.1666666667 Combine like terms: 1.424000624 + -0.1666666667 = 1.2573339573 x = 1.2573339573 Simplifying x = 1.2573339573Subproblem 2
x + 0.1666666667 = -1.424000624 Simplifying x + 0.1666666667 = -1.424000624 Reorder the terms: 0.1666666667 + x = -1.424000624 Solving 0.1666666667 + x = -1.424000624 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 = -1.424000624 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = -1.424000624 + -0.1666666667 x = -1.424000624 + -0.1666666667 Combine like terms: -1.424000624 + -0.1666666667 = -1.5906672907 x = -1.5906672907 Simplifying x = -1.5906672907Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2573339573, -1.5906672907}
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