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Simplifying x(16x + 1) = 6 Reorder the terms: x(1 + 16x) = 6 (1 * x + 16x * x) = 6 (1x + 16x2) = 6 Solving 1x + 16x2 = 6 Solving for variable 'x'. Reorder the terms: -6 + 1x + 16x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + 1x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.375 + 0.0625x + x2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + 0.0625x + 0.375 + x2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + 0.0625x + x2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + 0.0625x + x2 = 0 + 0.375 0.0625x + x2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 0.0625x + x2 = 0.375 The x term is 0.0625x. Take half its coefficient (0.03125). Square it (0.0009765625) and add it to both sides. Add '0.0009765625' to each side of the equation. 0.0625x + 0.0009765625 + x2 = 0.375 + 0.0009765625 Reorder the terms: 0.0009765625 + 0.0625x + x2 = 0.375 + 0.0009765625 Combine like terms: 0.375 + 0.0009765625 = 0.3759765625 0.0009765625 + 0.0625x + x2 = 0.3759765625 Factor a perfect square on the left side: (x + 0.03125)(x + 0.03125) = 0.3759765625 Calculate the square root of the right side: 0.613169277 Break this problem into two subproblems by setting (x + 0.03125) equal to 0.613169277 and -0.613169277.Subproblem 1
x + 0.03125 = 0.613169277 Simplifying x + 0.03125 = 0.613169277 Reorder the terms: 0.03125 + x = 0.613169277 Solving 0.03125 + x = 0.613169277 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03125' to each side of the equation. 0.03125 + -0.03125 + x = 0.613169277 + -0.03125 Combine like terms: 0.03125 + -0.03125 = 0.00000 0.00000 + x = 0.613169277 + -0.03125 x = 0.613169277 + -0.03125 Combine like terms: 0.613169277 + -0.03125 = 0.581919277 x = 0.581919277 Simplifying x = 0.581919277Subproblem 2
x + 0.03125 = -0.613169277 Simplifying x + 0.03125 = -0.613169277 Reorder the terms: 0.03125 + x = -0.613169277 Solving 0.03125 + x = -0.613169277 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03125' to each side of the equation. 0.03125 + -0.03125 + x = -0.613169277 + -0.03125 Combine like terms: 0.03125 + -0.03125 = 0.00000 0.00000 + x = -0.613169277 + -0.03125 x = -0.613169277 + -0.03125 Combine like terms: -0.613169277 + -0.03125 = -0.644419277 x = -0.644419277 Simplifying x = -0.644419277Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.581919277, -0.644419277}
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