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Simplifying 12x2 + 14x = 33 Reorder the terms: 14x + 12x2 = 33 Solving 14x + 12x2 = 33 Solving for variable 'x'. Reorder the terms: -33 + 14x + 12x2 = 33 + -33 Combine like terms: 33 + -33 = 0 -33 + 14x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -2.75 + 1.166666667x + x2 = 0 Move the constant term to the right: Add '2.75' to each side of the equation. -2.75 + 1.166666667x + 2.75 + x2 = 0 + 2.75 Reorder the terms: -2.75 + 2.75 + 1.166666667x + x2 = 0 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + 1.166666667x + x2 = 0 + 2.75 1.166666667x + x2 = 0 + 2.75 Combine like terms: 0 + 2.75 = 2.75 1.166666667x + x2 = 2.75 The x term is 1.166666667x. Take half its coefficient (0.5833333335). Square it (0.3402777780) and add it to both sides. Add '0.3402777780' to each side of the equation. 1.166666667x + 0.3402777780 + x2 = 2.75 + 0.3402777780 Reorder the terms: 0.3402777780 + 1.166666667x + x2 = 2.75 + 0.3402777780 Combine like terms: 2.75 + 0.3402777780 = 3.090277778 0.3402777780 + 1.166666667x + x2 = 3.090277778 Factor a perfect square on the left side: (x + 0.5833333335)(x + 0.5833333335) = 3.090277778 Calculate the square root of the right side: 1.757918593 Break this problem into two subproblems by setting (x + 0.5833333335) equal to 1.757918593 and -1.757918593.Subproblem 1
x + 0.5833333335 = 1.757918593 Simplifying x + 0.5833333335 = 1.757918593 Reorder the terms: 0.5833333335 + x = 1.757918593 Solving 0.5833333335 + x = 1.757918593 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5833333335' to each side of the equation. 0.5833333335 + -0.5833333335 + x = 1.757918593 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x = 1.757918593 + -0.5833333335 x = 1.757918593 + -0.5833333335 Combine like terms: 1.757918593 + -0.5833333335 = 1.1745852595 x = 1.1745852595 Simplifying x = 1.1745852595Subproblem 2
x + 0.5833333335 = -1.757918593 Simplifying x + 0.5833333335 = -1.757918593 Reorder the terms: 0.5833333335 + x = -1.757918593 Solving 0.5833333335 + x = -1.757918593 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5833333335' to each side of the equation. 0.5833333335 + -0.5833333335 + x = -1.757918593 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x = -1.757918593 + -0.5833333335 x = -1.757918593 + -0.5833333335 Combine like terms: -1.757918593 + -0.5833333335 = -2.3412519265 x = -2.3412519265 Simplifying x = -2.3412519265Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1745852595, -2.3412519265}
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