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Simplifying 8(4x + -1)(4x + -1) + 3 = -10(4x + -1) Reorder the terms: 8(-1 + 4x)(4x + -1) + 3 = -10(4x + -1) Reorder the terms: 8(-1 + 4x)(-1 + 4x) + 3 = -10(4x + -1) Multiply (-1 + 4x) * (-1 + 4x) 8(-1(-1 + 4x) + 4x * (-1 + 4x)) + 3 = -10(4x + -1) 8((-1 * -1 + 4x * -1) + 4x * (-1 + 4x)) + 3 = -10(4x + -1) 8((1 + -4x) + 4x * (-1 + 4x)) + 3 = -10(4x + -1) 8(1 + -4x + (-1 * 4x + 4x * 4x)) + 3 = -10(4x + -1) 8(1 + -4x + (-4x + 16x2)) + 3 = -10(4x + -1) Combine like terms: -4x + -4x = -8x 8(1 + -8x + 16x2) + 3 = -10(4x + -1) (1 * 8 + -8x * 8 + 16x2 * 8) + 3 = -10(4x + -1) (8 + -64x + 128x2) + 3 = -10(4x + -1) Reorder the terms: 8 + 3 + -64x + 128x2 = -10(4x + -1) Combine like terms: 8 + 3 = 11 11 + -64x + 128x2 = -10(4x + -1) Reorder the terms: 11 + -64x + 128x2 = -10(-1 + 4x) 11 + -64x + 128x2 = (-1 * -10 + 4x * -10) 11 + -64x + 128x2 = (10 + -40x) Solving 11 + -64x + 128x2 = 10 + -40x Solving for variable 'x'. Reorder the terms: 11 + -10 + -64x + 40x + 128x2 = 10 + -40x + -10 + 40x Combine like terms: 11 + -10 = 1 1 + -64x + 40x + 128x2 = 10 + -40x + -10 + 40x Combine like terms: -64x + 40x = -24x 1 + -24x + 128x2 = 10 + -40x + -10 + 40x Reorder the terms: 1 + -24x + 128x2 = 10 + -10 + -40x + 40x Combine like terms: 10 + -10 = 0 1 + -24x + 128x2 = 0 + -40x + 40x 1 + -24x + 128x2 = -40x + 40x Combine like terms: -40x + 40x = 0 1 + -24x + 128x2 = 0 Factor a trinomial. (1 + -16x)(1 + -8x) = 0Subproblem 1
Set the factor '(1 + -16x)' equal to zero and attempt to solve: Simplifying 1 + -16x = 0 Solving 1 + -16x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -16x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -16x = 0 + -1 -16x = 0 + -1 Combine like terms: 0 + -1 = -1 -16x = -1 Divide each side by '-16'. x = 0.0625 Simplifying x = 0.0625Subproblem 2
Set the factor '(1 + -8x)' equal to zero and attempt to solve: Simplifying 1 + -8x = 0 Solving 1 + -8x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -8x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -8x = 0 + -1 -8x = 0 + -1 Combine like terms: 0 + -1 = -1 -8x = -1 Divide each side by '-8'. x = 0.125 Simplifying x = 0.125Solution
x = {0.0625, 0.125}
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