0=16x^2+8x+1

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Solution for 0=16x^2+8x+1 equation:


Simplifying
0 = 16x2 + 8x + 1

Reorder the terms:
0 = 1 + 8x + 16x2

Solving
0 = 1 + 8x + 16x2

Solving for variable 'x'.

Combine like terms: 0 + -1 = -1
-1 + -8x + -16x2 = 1 + 8x + 16x2 + -1 + -8x + -16x2

Reorder the terms:
-1 + -8x + -16x2 = 1 + -1 + 8x + -8x + 16x2 + -16x2

Combine like terms: 1 + -1 = 0
-1 + -8x + -16x2 = 0 + 8x + -8x + 16x2 + -16x2
-1 + -8x + -16x2 = 8x + -8x + 16x2 + -16x2

Combine like terms: 8x + -8x = 0
-1 + -8x + -16x2 = 0 + 16x2 + -16x2
-1 + -8x + -16x2 = 16x2 + -16x2

Combine like terms: 16x2 + -16x2 = 0
-1 + -8x + -16x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1 + 8x + 16x2) = 0

Factor a trinomial.
-1((1 + 4x)(1 + 4x)) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(1 + 4x)' equal to zero and attempt to solve: Simplifying 1 + 4x = 0 Solving 1 + 4x = 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 + 4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4x = 0 + -1 4x = 0 + -1 Combine like terms: 0 + -1 = -1 4x = -1 Divide each side by '4'. x = -0.25 Simplifying x = -0.25

Subproblem 2

Set the factor '(1 + 4x)' equal to zero and attempt to solve: Simplifying 1 + 4x = 0 Solving 1 + 4x = 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 + 4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4x = 0 + -1 4x = 0 + -1 Combine like terms: 0 + -1 = -1 4x = -1 Divide each side by '4'. x = -0.25 Simplifying x = -0.25

Solution

x = {-0.25, -0.25}

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