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Simplifying 4x * x * 4 * 4 = 2x + 2 * 2 Reorder the terms for easier multiplication: 4 * 4 * 4x * x = 2x + 2 * 2 Multiply 4 * 4 16 * 4x * x = 2x + 2 * 2 Multiply 16 * 4 64x * x = 2x + 2 * 2 Multiply x * x 64x2 = 2x + 2 * 2 Multiply 2 * 2 64x2 = 2x + 4 Reorder the terms: 64x2 = 4 + 2x Solving 64x2 = 4 + 2x Solving for variable 'x'. Reorder the terms: -4 + -2x + 64x2 = 4 + 2x + -4 + -2x Reorder the terms: -4 + -2x + 64x2 = 4 + -4 + 2x + -2x Combine like terms: 4 + -4 = 0 -4 + -2x + 64x2 = 0 + 2x + -2x -4 + -2x + 64x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -4 + -2x + 64x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + -1x + 32x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + -1x + 32x2)' equal to zero and attempt to solve: Simplifying -2 + -1x + 32x2 = 0 Solving -2 + -1x + 32x2 = 0 Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. -0.0625 + -0.03125x + x2 = 0 Move the constant term to the right: Add '0.0625' to each side of the equation. -0.0625 + -0.03125x + 0.0625 + x2 = 0 + 0.0625 Reorder the terms: -0.0625 + 0.0625 + -0.03125x + x2 = 0 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + -0.03125x + x2 = 0 + 0.0625 -0.03125x + x2 = 0 + 0.0625 Combine like terms: 0 + 0.0625 = 0.0625 -0.03125x + x2 = 0.0625 The x term is -0.03125x. Take half its coefficient (-0.015625). Square it (0.000244140625) and add it to both sides. Add '0.000244140625' to each side of the equation. -0.03125x + 0.000244140625 + x2 = 0.0625 + 0.000244140625 Reorder the terms: 0.000244140625 + -0.03125x + x2 = 0.0625 + 0.000244140625 Combine like terms: 0.0625 + 0.000244140625 = 0.062744140625 0.000244140625 + -0.03125x + x2 = 0.062744140625 Factor a perfect square on the left side: (x + -0.015625)(x + -0.015625) = 0.062744140625 Calculate the square root of the right side: 0.250487805 Break this problem into two subproblems by setting (x + -0.015625) equal to 0.250487805 and -0.250487805.Subproblem 1
x + -0.015625 = 0.250487805 Simplifying x + -0.015625 = 0.250487805 Reorder the terms: -0.015625 + x = 0.250487805 Solving -0.015625 + x = 0.250487805 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.015625' to each side of the equation. -0.015625 + 0.015625 + x = 0.250487805 + 0.015625 Combine like terms: -0.015625 + 0.015625 = 0.000000 0.000000 + x = 0.250487805 + 0.015625 x = 0.250487805 + 0.015625 Combine like terms: 0.250487805 + 0.015625 = 0.266112805 x = 0.266112805 Simplifying x = 0.266112805Subproblem 2
x + -0.015625 = -0.250487805 Simplifying x + -0.015625 = -0.250487805 Reorder the terms: -0.015625 + x = -0.250487805 Solving -0.015625 + x = -0.250487805 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.015625' to each side of the equation. -0.015625 + 0.015625 + x = -0.250487805 + 0.015625 Combine like terms: -0.015625 + 0.015625 = 0.000000 0.000000 + x = -0.250487805 + 0.015625 x = -0.250487805 + 0.015625 Combine like terms: -0.250487805 + 0.015625 = -0.234862805 x = -0.234862805 Simplifying x = -0.234862805Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.266112805, -0.234862805}Solution
x = {0.266112805, -0.234862805}
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