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Simplifying 6x2 + 5x + -33 = 0 Reorder the terms: -33 + 5x + 6x2 = 0 Solving -33 + 5x + 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 + 0.8333333333x + x2 = 0 Move the constant term to the right: Add '5.5' to each side of the equation. -5.5 + 0.8333333333x + 5.5 + x2 = 0 + 5.5 Reorder the terms: -5.5 + 5.5 + 0.8333333333x + x2 = 0 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + 0.8333333333x + x2 = 0 + 5.5 0.8333333333x + x2 = 0 + 5.5 Combine like terms: 0 + 5.5 = 5.5 0.8333333333x + x2 = 5.5 The x term is 0.8333333333x. Take half its coefficient (0.4166666667). Square it (0.1736111111) and add it to both sides. Add '0.1736111111' to each side of the equation. 0.8333333333x + 0.1736111111 + x2 = 5.5 + 0.1736111111 Reorder the terms: 0.1736111111 + 0.8333333333x + x2 = 5.5 + 0.1736111111 Combine like terms: 5.5 + 0.1736111111 = 5.6736111111 0.1736111111 + 0.8333333333x + x2 = 5.6736111111 Factor a perfect square on the left side: (x + 0.4166666667)(x + 0.4166666667) = 5.6736111111 Calculate the square root of the right side: 2.381934321 Break this problem into two subproblems by setting (x + 0.4166666667) equal to 2.381934321 and -2.381934321.Subproblem 1
x + 0.4166666667 = 2.381934321 Simplifying x + 0.4166666667 = 2.381934321 Reorder the terms: 0.4166666667 + x = 2.381934321 Solving 0.4166666667 + x = 2.381934321 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4166666667' to each side of the equation. 0.4166666667 + -0.4166666667 + x = 2.381934321 + -0.4166666667 Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000 0.0000000000 + x = 2.381934321 + -0.4166666667 x = 2.381934321 + -0.4166666667 Combine like terms: 2.381934321 + -0.4166666667 = 1.9652676543 x = 1.9652676543 Simplifying x = 1.9652676543Subproblem 2
x + 0.4166666667 = -2.381934321 Simplifying x + 0.4166666667 = -2.381934321 Reorder the terms: 0.4166666667 + x = -2.381934321 Solving 0.4166666667 + x = -2.381934321 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4166666667' to each side of the equation. 0.4166666667 + -0.4166666667 + x = -2.381934321 + -0.4166666667 Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000 0.0000000000 + x = -2.381934321 + -0.4166666667 x = -2.381934321 + -0.4166666667 Combine like terms: -2.381934321 + -0.4166666667 = -2.7986009877 x = -2.7986009877 Simplifying x = -2.7986009877Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.9652676543, -2.7986009877}
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