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Simplifying 16x2 + 64x + 6 = 0 Reorder the terms: 6 + 64x + 16x2 = 0 Solving 6 + 64x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 32x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + 32x + 8x2)' equal to zero and attempt to solve: Simplifying 3 + 32x + 8x2 = 0 Solving 3 + 32x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.375 + 4x + x2 = 0 Move the constant term to the right: Add '-0.375' to each side of the equation. 0.375 + 4x + -0.375 + x2 = 0 + -0.375 Reorder the terms: 0.375 + -0.375 + 4x + x2 = 0 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + 4x + x2 = 0 + -0.375 4x + x2 = 0 + -0.375 Combine like terms: 0 + -0.375 = -0.375 4x + x2 = -0.375 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = -0.375 + 4 Reorder the terms: 4 + 4x + x2 = -0.375 + 4 Combine like terms: -0.375 + 4 = 3.625 4 + 4x + x2 = 3.625 Factor a perfect square on the left side: (x + 2)(x + 2) = 3.625 Calculate the square root of the right side: 1.903943276 Break this problem into two subproblems by setting (x + 2) equal to 1.903943276 and -1.903943276.Subproblem 1
x + 2 = 1.903943276 Simplifying x + 2 = 1.903943276 Reorder the terms: 2 + x = 1.903943276 Solving 2 + x = 1.903943276 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 1.903943276 + -2 Combine like terms: 2 + -2 = 0 0 + x = 1.903943276 + -2 x = 1.903943276 + -2 Combine like terms: 1.903943276 + -2 = -0.096056724 x = -0.096056724 Simplifying x = -0.096056724Subproblem 2
x + 2 = -1.903943276 Simplifying x + 2 = -1.903943276 Reorder the terms: 2 + x = -1.903943276 Solving 2 + x = -1.903943276 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -1.903943276 + -2 Combine like terms: 2 + -2 = 0 0 + x = -1.903943276 + -2 x = -1.903943276 + -2 Combine like terms: -1.903943276 + -2 = -3.903943276 x = -3.903943276 Simplifying x = -3.903943276Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.096056724, -3.903943276}Solution
x = {-0.096056724, -3.903943276}
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