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Simplifying 8x(4x + -1) = 3 Reorder the terms: 8x(-1 + 4x) = 3 (-1 * 8x + 4x * 8x) = 3 (-8x + 32x2) = 3 Solving -8x + 32x2 = 3 Solving for variable 'x'. Reorder the terms: -3 + -8x + 32x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + -8x + 32x2 = 0 Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. -0.09375 + -0.25x + x2 = 0 Move the constant term to the right: Add '0.09375' to each side of the equation. -0.09375 + -0.25x + 0.09375 + x2 = 0 + 0.09375 Reorder the terms: -0.09375 + 0.09375 + -0.25x + x2 = 0 + 0.09375 Combine like terms: -0.09375 + 0.09375 = 0.00000 0.00000 + -0.25x + x2 = 0 + 0.09375 -0.25x + x2 = 0 + 0.09375 Combine like terms: 0 + 0.09375 = 0.09375 -0.25x + x2 = 0.09375 The x term is -0.25x. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25x + 0.015625 + x2 = 0.09375 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = 0.09375 + 0.015625 Combine like terms: 0.09375 + 0.015625 = 0.109375 0.015625 + -0.25x + x2 = 0.109375 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = 0.109375 Calculate the square root of the right side: 0.330718914 Break this problem into two subproblems by setting (x + -0.125) equal to 0.330718914 and -0.330718914.Subproblem 1
x + -0.125 = 0.330718914 Simplifying x + -0.125 = 0.330718914 Reorder the terms: -0.125 + x = 0.330718914 Solving -0.125 + x = 0.330718914 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 0.330718914 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 0.330718914 + 0.125 x = 0.330718914 + 0.125 Combine like terms: 0.330718914 + 0.125 = 0.455718914 x = 0.455718914 Simplifying x = 0.455718914Subproblem 2
x + -0.125 = -0.330718914 Simplifying x + -0.125 = -0.330718914 Reorder the terms: -0.125 + x = -0.330718914 Solving -0.125 + x = -0.330718914 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -0.330718914 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -0.330718914 + 0.125 x = -0.330718914 + 0.125 Combine like terms: -0.330718914 + 0.125 = -0.205718914 x = -0.205718914 Simplifying x = -0.205718914Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.455718914, -0.205718914}
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