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Simplifying 16(4x2 + -4x + 1) + 3 = -16(2x + -1) Reorder the terms: 16(1 + -4x + 4x2) + 3 = -16(2x + -1) (1 * 16 + -4x * 16 + 4x2 * 16) + 3 = -16(2x + -1) (16 + -64x + 64x2) + 3 = -16(2x + -1) Reorder the terms: 16 + 3 + -64x + 64x2 = -16(2x + -1) Combine like terms: 16 + 3 = 19 19 + -64x + 64x2 = -16(2x + -1) Reorder the terms: 19 + -64x + 64x2 = -16(-1 + 2x) 19 + -64x + 64x2 = (-1 * -16 + 2x * -16) 19 + -64x + 64x2 = (16 + -32x) Solving 19 + -64x + 64x2 = 16 + -32x Solving for variable 'x'. Reorder the terms: 19 + -16 + -64x + 32x + 64x2 = 16 + -32x + -16 + 32x Combine like terms: 19 + -16 = 3 3 + -64x + 32x + 64x2 = 16 + -32x + -16 + 32x Combine like terms: -64x + 32x = -32x 3 + -32x + 64x2 = 16 + -32x + -16 + 32x Reorder the terms: 3 + -32x + 64x2 = 16 + -16 + -32x + 32x Combine like terms: 16 + -16 = 0 3 + -32x + 64x2 = 0 + -32x + 32x 3 + -32x + 64x2 = -32x + 32x Combine like terms: -32x + 32x = 0 3 + -32x + 64x2 = 0 Factor a trinomial. (1 + -8x)(3 + -8x) = 0Subproblem 1
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 = 0.125Subproblem 2
Set the factor '(3 + -8x)' equal to zero and attempt to solve: Simplifying 3 + -8x = 0 Solving 3 + -8x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -8x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -8x = 0 + -3 -8x = 0 + -3 Combine like terms: 0 + -3 = -3 -8x = -3 Divide each side by '-8'. x = 0.375 Simplifying x = 0.375Solution
x = {0.125, 0.375}
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