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Simplifying 3x2 + 9x + -44 = 0 Reorder the terms: -44 + 9x + 3x2 = 0 Solving -44 + 9x + 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'. -14.66666667 + 3x + x2 = 0 Move the constant term to the right: Add '14.66666667' to each side of the equation. -14.66666667 + 3x + 14.66666667 + x2 = 0 + 14.66666667 Reorder the terms: -14.66666667 + 14.66666667 + 3x + x2 = 0 + 14.66666667 Combine like terms: -14.66666667 + 14.66666667 = 0.00000000 0.00000000 + 3x + x2 = 0 + 14.66666667 3x + x2 = 0 + 14.66666667 Combine like terms: 0 + 14.66666667 = 14.66666667 3x + x2 = 14.66666667 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 14.66666667 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 14.66666667 + 2.25 Combine like terms: 14.66666667 + 2.25 = 16.91666667 2.25 + 3x + x2 = 16.91666667 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 16.91666667 Calculate the square root of the right side: 4.11298756 Break this problem into two subproblems by setting (x + 1.5) equal to 4.11298756 and -4.11298756.Subproblem 1
x + 1.5 = 4.11298756 Simplifying x + 1.5 = 4.11298756 Reorder the terms: 1.5 + x = 4.11298756 Solving 1.5 + x = 4.11298756 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 4.11298756 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 4.11298756 + -1.5 x = 4.11298756 + -1.5 Combine like terms: 4.11298756 + -1.5 = 2.61298756 x = 2.61298756 Simplifying x = 2.61298756Subproblem 2
x + 1.5 = -4.11298756 Simplifying x + 1.5 = -4.11298756 Reorder the terms: 1.5 + x = -4.11298756 Solving 1.5 + x = -4.11298756 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -4.11298756 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -4.11298756 + -1.5 x = -4.11298756 + -1.5 Combine like terms: -4.11298756 + -1.5 = -5.61298756 x = -5.61298756 Simplifying x = -5.61298756Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.61298756, -5.61298756}
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