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Simplifying -2 + 11x(3x + 4) = 0 Reorder the terms: -2 + 11x(4 + 3x) = 0 -2 + (4 * 11x + 3x * 11x) = 0 -2 + (44x + 33x2) = 0 Solving -2 + 44x + 33x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 33 the coefficient of the squared term: Divide each side by '33'. -0.06060606061 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '0.06060606061' to each side of the equation. -0.06060606061 + 1.333333333x + 0.06060606061 + x2 = 0 + 0.06060606061 Reorder the terms: -0.06060606061 + 0.06060606061 + 1.333333333x + x2 = 0 + 0.06060606061 Combine like terms: -0.06060606061 + 0.06060606061 = 0.00000000000 0.00000000000 + 1.333333333x + x2 = 0 + 0.06060606061 1.333333333x + x2 = 0 + 0.06060606061 Combine like terms: 0 + 0.06060606061 = 0.06060606061 1.333333333x + x2 = 0.06060606061 The x term is 1.333333333x. Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. 1.333333333x + 0.4444444442 + x2 = 0.06060606061 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = 0.06060606061 + 0.4444444442 Combine like terms: 0.06060606061 + 0.4444444442 = 0.50505050481 0.4444444442 + 1.333333333x + x2 = 0.50505050481 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = 0.50505050481 Calculate the square root of the right side: 0.710669054 Break this problem into two subproblems by setting (x + 0.6666666665) equal to 0.710669054 and -0.710669054.Subproblem 1
x + 0.6666666665 = 0.710669054 Simplifying x + 0.6666666665 = 0.710669054 Reorder the terms: 0.6666666665 + x = 0.710669054 Solving 0.6666666665 + x = 0.710669054 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = 0.710669054 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 0.710669054 + -0.6666666665 x = 0.710669054 + -0.6666666665 Combine like terms: 0.710669054 + -0.6666666665 = 0.0440023875 x = 0.0440023875 Simplifying x = 0.0440023875Subproblem 2
x + 0.6666666665 = -0.710669054 Simplifying x + 0.6666666665 = -0.710669054 Reorder the terms: 0.6666666665 + x = -0.710669054 Solving 0.6666666665 + x = -0.710669054 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = -0.710669054 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -0.710669054 + -0.6666666665 x = -0.710669054 + -0.6666666665 Combine like terms: -0.710669054 + -0.6666666665 = -1.3773357205 x = -1.3773357205 Simplifying x = -1.3773357205Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.0440023875, -1.3773357205}
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