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Simplifying 9x2 + -14x + -33 = 0 Reorder the terms: -33 + -14x + 9x2 = 0 Solving -33 + -14x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -3.666666667 + -1.555555556x + x2 = 0 Move the constant term to the right: Add '3.666666667' to each side of the equation. -3.666666667 + -1.555555556x + 3.666666667 + x2 = 0 + 3.666666667 Reorder the terms: -3.666666667 + 3.666666667 + -1.555555556x + x2 = 0 + 3.666666667 Combine like terms: -3.666666667 + 3.666666667 = 0.000000000 0.000000000 + -1.555555556x + x2 = 0 + 3.666666667 -1.555555556x + x2 = 0 + 3.666666667 Combine like terms: 0 + 3.666666667 = 3.666666667 -1.555555556x + x2 = 3.666666667 The x term is -1.555555556x. Take half its coefficient (-0.777777778). Square it (0.6049382720) and add it to both sides. Add '0.6049382720' to each side of the equation. -1.555555556x + 0.6049382720 + x2 = 3.666666667 + 0.6049382720 Reorder the terms: 0.6049382720 + -1.555555556x + x2 = 3.666666667 + 0.6049382720 Combine like terms: 3.666666667 + 0.6049382720 = 4.271604939 0.6049382720 + -1.555555556x + x2 = 4.271604939 Factor a perfect square on the left side: (x + -0.777777778)(x + -0.777777778) = 4.271604939 Calculate the square root of the right side: 2.066786138 Break this problem into two subproblems by setting (x + -0.777777778) equal to 2.066786138 and -2.066786138.Subproblem 1
x + -0.777777778 = 2.066786138 Simplifying x + -0.777777778 = 2.066786138 Reorder the terms: -0.777777778 + x = 2.066786138 Solving -0.777777778 + x = 2.066786138 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.777777778' to each side of the equation. -0.777777778 + 0.777777778 + x = 2.066786138 + 0.777777778 Combine like terms: -0.777777778 + 0.777777778 = 0.000000000 0.000000000 + x = 2.066786138 + 0.777777778 x = 2.066786138 + 0.777777778 Combine like terms: 2.066786138 + 0.777777778 = 2.844563916 x = 2.844563916 Simplifying x = 2.844563916Subproblem 2
x + -0.777777778 = -2.066786138 Simplifying x + -0.777777778 = -2.066786138 Reorder the terms: -0.777777778 + x = -2.066786138 Solving -0.777777778 + x = -2.066786138 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.777777778' to each side of the equation. -0.777777778 + 0.777777778 + x = -2.066786138 + 0.777777778 Combine like terms: -0.777777778 + 0.777777778 = 0.000000000 0.000000000 + x = -2.066786138 + 0.777777778 x = -2.066786138 + 0.777777778 Combine like terms: -2.066786138 + 0.777777778 = -1.28900836 x = -1.28900836 Simplifying x = -1.28900836Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.844563916, -1.28900836}
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