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Simplifying 13x2 + -4x + -33 = 0 Reorder the terms: -33 + -4x + 13x2 = 0 Solving -33 + -4x + 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'. -2.538461538 + -0.3076923077x + x2 = 0 Move the constant term to the right: Add '2.538461538' to each side of the equation. -2.538461538 + -0.3076923077x + 2.538461538 + x2 = 0 + 2.538461538 Reorder the terms: -2.538461538 + 2.538461538 + -0.3076923077x + x2 = 0 + 2.538461538 Combine like terms: -2.538461538 + 2.538461538 = 0.000000000 0.000000000 + -0.3076923077x + x2 = 0 + 2.538461538 -0.3076923077x + x2 = 0 + 2.538461538 Combine like terms: 0 + 2.538461538 = 2.538461538 -0.3076923077x + x2 = 2.538461538 The x term is -0.3076923077x. Take half its coefficient (-0.1538461539). Square it (0.02366863907) and add it to both sides. Add '0.02366863907' to each side of the equation. -0.3076923077x + 0.02366863907 + x2 = 2.538461538 + 0.02366863907 Reorder the terms: 0.02366863907 + -0.3076923077x + x2 = 2.538461538 + 0.02366863907 Combine like terms: 2.538461538 + 0.02366863907 = 2.56213017707 0.02366863907 + -0.3076923077x + x2 = 2.56213017707 Factor a perfect square on the left side: (x + -0.1538461539)(x + -0.1538461539) = 2.56213017707 Calculate the square root of the right side: 1.600665542 Break this problem into two subproblems by setting (x + -0.1538461539) equal to 1.600665542 and -1.600665542.Subproblem 1
x + -0.1538461539 = 1.600665542 Simplifying x + -0.1538461539 = 1.600665542 Reorder the terms: -0.1538461539 + x = 1.600665542 Solving -0.1538461539 + x = 1.600665542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1538461539' to each side of the equation. -0.1538461539 + 0.1538461539 + x = 1.600665542 + 0.1538461539 Combine like terms: -0.1538461539 + 0.1538461539 = 0.0000000000 0.0000000000 + x = 1.600665542 + 0.1538461539 x = 1.600665542 + 0.1538461539 Combine like terms: 1.600665542 + 0.1538461539 = 1.7545116959 x = 1.7545116959 Simplifying x = 1.7545116959Subproblem 2
x + -0.1538461539 = -1.600665542 Simplifying x + -0.1538461539 = -1.600665542 Reorder the terms: -0.1538461539 + x = -1.600665542 Solving -0.1538461539 + x = -1.600665542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1538461539' to each side of the equation. -0.1538461539 + 0.1538461539 + x = -1.600665542 + 0.1538461539 Combine like terms: -0.1538461539 + 0.1538461539 = 0.0000000000 0.0000000000 + x = -1.600665542 + 0.1538461539 x = -1.600665542 + 0.1538461539 Combine like terms: -1.600665542 + 0.1538461539 = -1.4468193881 x = -1.4468193881 Simplifying x = -1.4468193881Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.7545116959, -1.4468193881}
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