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Simplifying 33x2 + -44x = -6 + 8 Reorder the terms: -44x + 33x2 = -6 + 8 Combine like terms: -6 + 8 = 2 -44x + 33x2 = 2 Solving -44x + 33x2 = 2 Solving for variable 'x'. Reorder the terms: -2 + -44x + 33x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + -44x + 33x2 = 0 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 = 1.3773357205 x = 1.3773357205 Simplifying x = 1.3773357205Subproblem 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 = -0.0440023875 x = -0.0440023875 Simplifying x = -0.0440023875Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3773357205, -0.0440023875}
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