x^2+.16x+.16=1

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Solution for x^2+.16x+.16=1 equation:


Simplifying
x2 + 0.16x + 0.16 = 1

Reorder the terms:
0.16 + 0.16x + x2 = 1

Solving
0.16 + 0.16x + x2 = 1

Solving for variable 'x'.

Reorder the terms:
0.16 + -1 + 0.16x + x2 = 1 + -1

Combine like terms: 0.16 + -1 = -0.84
-0.84 + 0.16x + x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-0.84 + 0.16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '0.84' to each side of the equation.
-0.84 + 0.16x + 0.84 + x2 = 0 + 0.84

Reorder the terms:
-0.84 + 0.84 + 0.16x + x2 = 0 + 0.84

Combine like terms: -0.84 + 0.84 = 0.00
0.00 + 0.16x + x2 = 0 + 0.84
0.16x + x2 = 0 + 0.84

Combine like terms: 0 + 0.84 = 0.84
0.16x + x2 = 0.84

The x term is 0.16x.  Take half its coefficient (0.08).
Square it (0.0064) and add it to both sides.

Add '0.0064' to each side of the equation.
0.16x + 0.0064 + x2 = 0.84 + 0.0064

Reorder the terms:
0.0064 + 0.16x + x2 = 0.84 + 0.0064

Combine like terms: 0.84 + 0.0064 = 0.8464
0.0064 + 0.16x + x2 = 0.8464

Factor a perfect square on the left side:
(x + 0.08)(x + 0.08) = 0.8464

Calculate the square root of the right side: 0.92

Break this problem into two subproblems by setting 
(x + 0.08) equal to 0.92 and -0.92.

Subproblem 1

x + 0.08 = 0.92 Simplifying x + 0.08 = 0.92 Reorder the terms: 0.08 + x = 0.92 Solving 0.08 + x = 0.92 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.08' to each side of the equation. 0.08 + -0.08 + x = 0.92 + -0.08 Combine like terms: 0.08 + -0.08 = 0.00 0.00 + x = 0.92 + -0.08 x = 0.92 + -0.08 Combine like terms: 0.92 + -0.08 = 0.84 x = 0.84 Simplifying x = 0.84

Subproblem 2

x + 0.08 = -0.92 Simplifying x + 0.08 = -0.92 Reorder the terms: 0.08 + x = -0.92 Solving 0.08 + x = -0.92 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.08' to each side of the equation. 0.08 + -0.08 + x = -0.92 + -0.08 Combine like terms: 0.08 + -0.08 = 0.00 0.00 + x = -0.92 + -0.08 x = -0.92 + -0.08 Combine like terms: -0.92 + -0.08 = -1 x = -1 Simplifying x = -1

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.84, -1}

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