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Simplifying 16x2 + 128x + 6 = 0 Reorder the terms: 6 + 128x + 16x2 = 0 Solving 6 + 128x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 64x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + 64x + 8x2)' equal to zero and attempt to solve: Simplifying 3 + 64x + 8x2 = 0 Solving 3 + 64x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.375 + 8x + x2 = 0 Move the constant term to the right: Add '-0.375' to each side of the equation. 0.375 + 8x + -0.375 + x2 = 0 + -0.375 Reorder the terms: 0.375 + -0.375 + 8x + x2 = 0 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + 8x + x2 = 0 + -0.375 8x + x2 = 0 + -0.375 Combine like terms: 0 + -0.375 = -0.375 8x + x2 = -0.375 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = -0.375 + 16 Reorder the terms: 16 + 8x + x2 = -0.375 + 16 Combine like terms: -0.375 + 16 = 15.625 16 + 8x + x2 = 15.625 Factor a perfect square on the left side: (x + 4)(x + 4) = 15.625 Calculate the square root of the right side: 3.952847075 Break this problem into two subproblems by setting (x + 4) equal to 3.952847075 and -3.952847075.Subproblem 1
x + 4 = 3.952847075 Simplifying x + 4 = 3.952847075 Reorder the terms: 4 + x = 3.952847075 Solving 4 + x = 3.952847075 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 3.952847075 + -4 Combine like terms: 4 + -4 = 0 0 + x = 3.952847075 + -4 x = 3.952847075 + -4 Combine like terms: 3.952847075 + -4 = -0.047152925 x = -0.047152925 Simplifying x = -0.047152925Subproblem 2
x + 4 = -3.952847075 Simplifying x + 4 = -3.952847075 Reorder the terms: 4 + x = -3.952847075 Solving 4 + x = -3.952847075 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -3.952847075 + -4 Combine like terms: 4 + -4 = 0 0 + x = -3.952847075 + -4 x = -3.952847075 + -4 Combine like terms: -3.952847075 + -4 = -7.952847075 x = -7.952847075 Simplifying x = -7.952847075Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.047152925, -7.952847075}Solution
x = {-0.047152925, -7.952847075}
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