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Simplifying 0 = 8x2 + 8x + 1 Reorder the terms: 0 = 1 + 8x + 8x2 Solving 0 = 1 + 8x + 8x2 Solving for variable 'x'. Combine like terms: 0 + -1 = -1 -1 + -8x + -8x2 = 1 + 8x + 8x2 + -1 + -8x + -8x2 Reorder the terms: -1 + -8x + -8x2 = 1 + -1 + 8x + -8x + 8x2 + -8x2 Combine like terms: 1 + -1 = 0 -1 + -8x + -8x2 = 0 + 8x + -8x + 8x2 + -8x2 -1 + -8x + -8x2 = 8x + -8x + 8x2 + -8x2 Combine like terms: 8x + -8x = 0 -1 + -8x + -8x2 = 0 + 8x2 + -8x2 -1 + -8x + -8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 -1 + -8x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(1 + 8x + 8x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(1 + 8x + 8x2)' equal to zero and attempt to solve: Simplifying 1 + 8x + 8x2 = 0 Solving 1 + 8x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.125 + x + x2 = 0 Move the constant term to the right: Add '-0.125' to each side of the equation. 0.125 + x + -0.125 + x2 = 0 + -0.125 Reorder the terms: 0.125 + -0.125 + x + x2 = 0 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x + x2 = 0 + -0.125 x + x2 = 0 + -0.125 Combine like terms: 0 + -0.125 = -0.125 x + x2 = -0.125 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = -0.125 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = -0.125 + 0.25 Combine like terms: -0.125 + 0.25 = 0.125 1.25 + x2 = 0.125 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.125 Calculate the square root of the right side: 0.353553391 Break this problem into two subproblems by setting (x + 0.5) equal to 0.353553391 and -0.353553391.Subproblem 1
x + 0.5 = 0.353553391 Simplifying x + 0.5 = 0.353553391 Reorder the terms: 0.5 + x = 0.353553391 Solving 0.5 + x = 0.353553391 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.353553391 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.353553391 + -0.5 x = 0.353553391 + -0.5 Combine like terms: 0.353553391 + -0.5 = -0.146446609 x = -0.146446609 Simplifying x = -0.146446609Subproblem 2
x + 0.5 = -0.353553391 Simplifying x + 0.5 = -0.353553391 Reorder the terms: 0.5 + x = -0.353553391 Solving 0.5 + x = -0.353553391 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.353553391 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.353553391 + -0.5 x = -0.353553391 + -0.5 Combine like terms: -0.353553391 + -0.5 = -0.853553391 x = -0.853553391 Simplifying x = -0.853553391Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.146446609, -0.853553391}Solution
x = {-0.146446609, -0.853553391}
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