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Simplifying 16x2 + 192x + 224 = 0 Reorder the terms: 224 + 192x + 16x2 = 0 Solving 224 + 192x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '16'. 16(14 + 12x + x2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(14 + 12x + x2)' equal to zero and attempt to solve: Simplifying 14 + 12x + x2 = 0 Solving 14 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + 12x + -14 + x2 = 0 + -14 Reorder the terms: 14 + -14 + 12x + x2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + 12x + x2 = 0 + -14 12x + x2 = 0 + -14 Combine like terms: 0 + -14 = -14 12x + x2 = -14 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = -14 + 36 Reorder the terms: 36 + 12x + x2 = -14 + 36 Combine like terms: -14 + 36 = 22 36 + 12x + x2 = 22 Factor a perfect square on the left side: (x + 6)(x + 6) = 22 Calculate the square root of the right side: 4.69041576 Break this problem into two subproblems by setting (x + 6) equal to 4.69041576 and -4.69041576.Subproblem 1
x + 6 = 4.69041576 Simplifying x + 6 = 4.69041576 Reorder the terms: 6 + x = 4.69041576 Solving 6 + x = 4.69041576 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 4.69041576 + -6 Combine like terms: 6 + -6 = 0 0 + x = 4.69041576 + -6 x = 4.69041576 + -6 Combine like terms: 4.69041576 + -6 = -1.30958424 x = -1.30958424 Simplifying x = -1.30958424Subproblem 2
x + 6 = -4.69041576 Simplifying x + 6 = -4.69041576 Reorder the terms: 6 + x = -4.69041576 Solving 6 + x = -4.69041576 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -4.69041576 + -6 Combine like terms: 6 + -6 = 0 0 + x = -4.69041576 + -6 x = -4.69041576 + -6 Combine like terms: -4.69041576 + -6 = -10.69041576 x = -10.69041576 Simplifying x = -10.69041576Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.30958424, -10.69041576}Solution
x = {-1.30958424, -10.69041576}
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