Answer:
Step-by-step explanation:
Simplifying
16x2 + -8x + 2 = 0
Reorder the terms:
2 + -8x + 16x2 = 0
Solving
2 + -8x + 16x2 = 0
Solving for variable 'x'.
Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -4x + 8x2) = 0
Ignore the factor 2.
Subproblem 1
Set the factor '(1 + -4x + 8x2)' equal to zero and attempt to solve:
Simplifying
1 + -4x + 8x2 = 0
Solving
1 + -4x + 8x2 = 0
Begin completing the square. Divide all terms by
8 the coefficient of the squared term:
Divide each side by '8'.
0.125 + -0.5x + x2 = 0
Move the constant term to the right:
Add '-0.125' to each side of the equation.
0.125 + -0.5x + -0.125 + x2 = 0 + -0.125
Reorder the terms:
0.125 + -0.125 + -0.5x + x2 = 0 + -0.125
Combine like terms: 0.125 + -0.125 = 0.000
0.000 + -0.5x + x2 = 0 + -0.125
-0.5x + x2 = 0 + -0.125
Combine like terms: 0 + -0.125 = -0.125
-0.5x + x2 = -0.125
The x term is -0.5x. Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.
Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = -0.125 + 0.0625
Reorder the terms:
0.0625 + -0.5x + x2 = -0.125 + 0.0625
Combine like terms: -0.125 + 0.0625 = -0.0625
0.0625 + -0.5x + x2 = -0.0625
Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = -0.0625
