16(x+.5)(x+.5)=1

Solution for 16(x+.5)(x+.5)=1 equation:

Simplifying
16(x + 0.5)(x + 0.5) = 1

Reorder the terms:
16(0.5 + x)(x + 0.5) = 1

Reorder the terms:
16(0.5 + x)(0.5 + x) = 1

Multiply (0.5 + x) * (0.5 + x)
16(0.5(0.5 + x) + x(0.5 + x)) = 1
16((0.5 * 0.5 + x * 0.5) + x(0.5 + x)) = 1
16((0.25 + 0.5x) + x(0.5 + x)) = 1
16(0.25 + 0.5x + (0.5 * x + x * x)) = 1
16(0.25 + 0.5x + (0.5x + x2)) = 1

Combine like terms: 0.5x + 0.5x = 1x
16(0.25 + 1x + x2) = 1
(0.25 * 16 + 1x * 16 + x2 * 16) = 1
(4 + 16x + 16x2) = 1

Solving
4 + 16x + 16x2 = 1

Solving for variable 'x'.

Reorder the terms:
4 + -1 + 16x + 16x2 = 1 + -1

Combine like terms: 4 + -1 = 3
3 + 16x + 16x2 = 1 + -1

Combine like terms: 1 + -1 = 0
3 + 16x + 16x2 = 0

Factor a trinomial.
(3 + 4x)(1 + 4x) = 0

Subproblem 1
Set the factor '(3 + 4x)' equal to zero and attempt to solve:

Simplifying
3 + 4x = 0

Solving
3 + 4x = 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 + 4x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4x = 0 + -3
4x = 0 + -3

Combine like terms: 0 + -3 = -3
4x = -3

Divide each side by '4'.
x = -0.75

Simplifying
x = -0.75
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 = {-0.75, -0.25}