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Simplifying 3x2 + 9x2 + -14x + -49 = 289 Reorder the terms: -49 + -14x + 3x2 + 9x2 = 289 Combine like terms: 3x2 + 9x2 = 12x2 -49 + -14x + 12x2 = 289 Solving -49 + -14x + 12x2 = 289 Solving for variable 'x'. Reorder the terms: -49 + -289 + -14x + 12x2 = 289 + -289 Combine like terms: -49 + -289 = -338 -338 + -14x + 12x2 = 289 + -289 Combine like terms: 289 + -289 = 0 -338 + -14x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-169 + -7x + 6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-169 + -7x + 6x2)' equal to zero and attempt to solve: Simplifying -169 + -7x + 6x2 = 0 Solving -169 + -7x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -28.16666667 + -1.166666667x + x2 = 0 Move the constant term to the right: Add '28.16666667' to each side of the equation. -28.16666667 + -1.166666667x + 28.16666667 + x2 = 0 + 28.16666667 Reorder the terms: -28.16666667 + 28.16666667 + -1.166666667x + x2 = 0 + 28.16666667 Combine like terms: -28.16666667 + 28.16666667 = 0.00000000 0.00000000 + -1.166666667x + x2 = 0 + 28.16666667 -1.166666667x + x2 = 0 + 28.16666667 Combine like terms: 0 + 28.16666667 = 28.16666667 -1.166666667x + x2 = 28.16666667 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 = 28.16666667 + 0.3402777780 Reorder the terms: 0.3402777780 + -1.166666667x + x2 = 28.16666667 + 0.3402777780 Combine like terms: 28.16666667 + 0.3402777780 = 28.506944448 0.3402777780 + -1.166666667x + x2 = 28.506944448 Factor a perfect square on the left side: (x + -0.5833333335)(x + -0.5833333335) = 28.506944448 Calculate the square root of the right side: 5.339189494 Break this problem into two subproblems by setting (x + -0.5833333335) equal to 5.339189494 and -5.339189494.Subproblem 1
x + -0.5833333335 = 5.339189494 Simplifying x + -0.5833333335 = 5.339189494 Reorder the terms: -0.5833333335 + x = 5.339189494 Solving -0.5833333335 + x = 5.339189494 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 = 5.339189494 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = 5.339189494 + 0.5833333335 x = 5.339189494 + 0.5833333335 Combine like terms: 5.339189494 + 0.5833333335 = 5.9225228275 x = 5.9225228275 Simplifying x = 5.9225228275Subproblem 2
x + -0.5833333335 = -5.339189494 Simplifying x + -0.5833333335 = -5.339189494 Reorder the terms: -0.5833333335 + x = -5.339189494 Solving -0.5833333335 + x = -5.339189494 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 = -5.339189494 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = -5.339189494 + 0.5833333335 x = -5.339189494 + 0.5833333335 Combine like terms: -5.339189494 + 0.5833333335 = -4.7558561605 x = -4.7558561605 Simplifying x = -4.7558561605Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.9225228275, -4.7558561605}Solution
x = {5.9225228275, -4.7558561605}
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