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Simplifying 6x2 + -35x + -33 = 0 Reorder the terms: -33 + -35x + 6x2 = 0 Solving -33 + -35x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -5.5 + -5.833333333x + x2 = 0 Move the constant term to the right: Add '5.5' to each side of the equation. -5.5 + -5.833333333x + 5.5 + x2 = 0 + 5.5 Reorder the terms: -5.5 + 5.5 + -5.833333333x + x2 = 0 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + -5.833333333x + x2 = 0 + 5.5 -5.833333333x + x2 = 0 + 5.5 Combine like terms: 0 + 5.5 = 5.5 -5.833333333x + x2 = 5.5 The x term is -5.833333333x. Take half its coefficient (-2.916666667). Square it (8.506944446) and add it to both sides. Add '8.506944446' to each side of the equation. -5.833333333x + 8.506944446 + x2 = 5.5 + 8.506944446 Reorder the terms: 8.506944446 + -5.833333333x + x2 = 5.5 + 8.506944446 Combine like terms: 5.5 + 8.506944446 = 14.006944446 8.506944446 + -5.833333333x + x2 = 14.006944446 Factor a perfect square on the left side: (x + -2.916666667)(x + -2.916666667) = 14.006944446 Calculate the square root of the right side: 3.742585262 Break this problem into two subproblems by setting (x + -2.916666667) equal to 3.742585262 and -3.742585262.Subproblem 1
x + -2.916666667 = 3.742585262 Simplifying x + -2.916666667 = 3.742585262 Reorder the terms: -2.916666667 + x = 3.742585262 Solving -2.916666667 + x = 3.742585262 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.916666667' to each side of the equation. -2.916666667 + 2.916666667 + x = 3.742585262 + 2.916666667 Combine like terms: -2.916666667 + 2.916666667 = 0.000000000 0.000000000 + x = 3.742585262 + 2.916666667 x = 3.742585262 + 2.916666667 Combine like terms: 3.742585262 + 2.916666667 = 6.659251929 x = 6.659251929 Simplifying x = 6.659251929Subproblem 2
x + -2.916666667 = -3.742585262 Simplifying x + -2.916666667 = -3.742585262 Reorder the terms: -2.916666667 + x = -3.742585262 Solving -2.916666667 + x = -3.742585262 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.916666667' to each side of the equation. -2.916666667 + 2.916666667 + x = -3.742585262 + 2.916666667 Combine like terms: -2.916666667 + 2.916666667 = 0.000000000 0.000000000 + x = -3.742585262 + 2.916666667 x = -3.742585262 + 2.916666667 Combine like terms: -3.742585262 + 2.916666667 = -0.825918595 x = -0.825918595 Simplifying x = -0.825918595Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.659251929, -0.825918595}
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