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Simplifying -3x2 + 33x + -89 = 0 Reorder the terms: -89 + 33x + -3x2 = 0 Solving -89 + 33x + -3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 29.66666667 + -11x + x2 = 0 Move the constant term to the right: Add '-29.66666667' to each side of the equation. 29.66666667 + -11x + -29.66666667 + x2 = 0 + -29.66666667 Reorder the terms: 29.66666667 + -29.66666667 + -11x + x2 = 0 + -29.66666667 Combine like terms: 29.66666667 + -29.66666667 = 0.00000000 0.00000000 + -11x + x2 = 0 + -29.66666667 -11x + x2 = 0 + -29.66666667 Combine like terms: 0 + -29.66666667 = -29.66666667 -11x + x2 = -29.66666667 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = -29.66666667 + 30.25 Reorder the terms: 30.25 + -11x + x2 = -29.66666667 + 30.25 Combine like terms: -29.66666667 + 30.25 = 0.58333333 30.25 + -11x + x2 = 0.58333333 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 0.58333333 Calculate the square root of the right side: 0.763762614 Break this problem into two subproblems by setting (x + -5.5) equal to 0.763762614 and -0.763762614.Subproblem 1
x + -5.5 = 0.763762614 Simplifying x + -5.5 = 0.763762614 Reorder the terms: -5.5 + x = 0.763762614 Solving -5.5 + x = 0.763762614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 0.763762614 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 0.763762614 + 5.5 x = 0.763762614 + 5.5 Combine like terms: 0.763762614 + 5.5 = 6.263762614 x = 6.263762614 Simplifying x = 6.263762614Subproblem 2
x + -5.5 = -0.763762614 Simplifying x + -5.5 = -0.763762614 Reorder the terms: -5.5 + x = -0.763762614 Solving -5.5 + x = -0.763762614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -0.763762614 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -0.763762614 + 5.5 x = -0.763762614 + 5.5 Combine like terms: -0.763762614 + 5.5 = 4.736237386 x = 4.736237386 Simplifying x = 4.736237386Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.263762614, 4.736237386}
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