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Simplifying (6x2 + -33x + -55) + (7x2 + 6x) = 0 Reorder the terms: (-55 + -33x + 6x2) + (7x2 + 6x) = 0 Remove parenthesis around (-55 + -33x + 6x2) -55 + -33x + 6x2 + (7x2 + 6x) = 0 Reorder the terms: -55 + -33x + 6x2 + (6x + 7x2) = 0 Remove parenthesis around (6x + 7x2) -55 + -33x + 6x2 + 6x + 7x2 = 0 Reorder the terms: -55 + -33x + 6x + 6x2 + 7x2 = 0 Combine like terms: -33x + 6x = -27x -55 + -27x + 6x2 + 7x2 = 0 Combine like terms: 6x2 + 7x2 = 13x2 -55 + -27x + 13x2 = 0 Solving -55 + -27x + 13x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -4.230769231 + -2.076923077x + x2 = 0 Move the constant term to the right: Add '4.230769231' to each side of the equation. -4.230769231 + -2.076923077x + 4.230769231 + x2 = 0 + 4.230769231 Reorder the terms: -4.230769231 + 4.230769231 + -2.076923077x + x2 = 0 + 4.230769231 Combine like terms: -4.230769231 + 4.230769231 = 0.000000000 0.000000000 + -2.076923077x + x2 = 0 + 4.230769231 -2.076923077x + x2 = 0 + 4.230769231 Combine like terms: 0 + 4.230769231 = 4.230769231 -2.076923077x + x2 = 4.230769231 The x term is -2.076923077x. Take half its coefficient (-1.038461539). Square it (1.078402368) and add it to both sides. Add '1.078402368' to each side of the equation. -2.076923077x + 1.078402368 + x2 = 4.230769231 + 1.078402368 Reorder the terms: 1.078402368 + -2.076923077x + x2 = 4.230769231 + 1.078402368 Combine like terms: 4.230769231 + 1.078402368 = 5.309171599 1.078402368 + -2.076923077x + x2 = 5.309171599 Factor a perfect square on the left side: (x + -1.038461539)(x + -1.038461539) = 5.309171599 Calculate the square root of the right side: 2.30416397 Break this problem into two subproblems by setting (x + -1.038461539) equal to 2.30416397 and -2.30416397.Subproblem 1
x + -1.038461539 = 2.30416397 Simplifying x + -1.038461539 = 2.30416397 Reorder the terms: -1.038461539 + x = 2.30416397 Solving -1.038461539 + x = 2.30416397 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.038461539' to each side of the equation. -1.038461539 + 1.038461539 + x = 2.30416397 + 1.038461539 Combine like terms: -1.038461539 + 1.038461539 = 0.000000000 0.000000000 + x = 2.30416397 + 1.038461539 x = 2.30416397 + 1.038461539 Combine like terms: 2.30416397 + 1.038461539 = 3.342625509 x = 3.342625509 Simplifying x = 3.342625509Subproblem 2
x + -1.038461539 = -2.30416397 Simplifying x + -1.038461539 = -2.30416397 Reorder the terms: -1.038461539 + x = -2.30416397 Solving -1.038461539 + x = -2.30416397 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.038461539' to each side of the equation. -1.038461539 + 1.038461539 + x = -2.30416397 + 1.038461539 Combine like terms: -1.038461539 + 1.038461539 = 0.000000000 0.000000000 + x = -2.30416397 + 1.038461539 x = -2.30416397 + 1.038461539 Combine like terms: -2.30416397 + 1.038461539 = -1.265702431 x = -1.265702431 Simplifying x = -1.265702431Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.342625509, -1.265702431}
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