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Simplifying 16x2 + 8x = 6 Reorder the terms: 8x + 16x2 = 6 Solving 8x + 16x2 = 6 Solving for variable 'x'. Reorder the terms: -6 + 8x + 16x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + 8x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + 4x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + 4x + 8x2)' equal to zero and attempt to solve: Simplifying -3 + 4x + 8x2 = 0 Solving -3 + 4x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.375 + 0.5x + x2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + 0.5x + 0.375 + x2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + 0.5x + x2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + 0.5x + x2 = 0 + 0.375 0.5x + x2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 0.5x + x2 = 0.375 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 0.375 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 0.375 + 0.0625 Combine like terms: 0.375 + 0.0625 = 0.4375 0.0625 + 0.5x + x2 = 0.4375 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 0.4375 Calculate the square root of the right side: 0.661437828 Break this problem into two subproblems by setting (x + 0.25) equal to 0.661437828 and -0.661437828.Subproblem 1
x + 0.25 = 0.661437828 Simplifying x + 0.25 = 0.661437828 Reorder the terms: 0.25 + x = 0.661437828 Solving 0.25 + x = 0.661437828 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 0.661437828 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 0.661437828 + -0.25 x = 0.661437828 + -0.25 Combine like terms: 0.661437828 + -0.25 = 0.411437828 x = 0.411437828 Simplifying x = 0.411437828Subproblem 2
x + 0.25 = -0.661437828 Simplifying x + 0.25 = -0.661437828 Reorder the terms: 0.25 + x = -0.661437828 Solving 0.25 + x = -0.661437828 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -0.661437828 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -0.661437828 + -0.25 x = -0.661437828 + -0.25 Combine like terms: -0.661437828 + -0.25 = -0.911437828 x = -0.911437828 Simplifying x = -0.911437828Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.411437828, -0.911437828}Solution
x = {0.411437828, -0.911437828}
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