0.16x^2+0.16x-0.26=0

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Solution for 0.16x^2+0.16x-0.26=0 equation:


Simplifying
0.16x2 + 0.16x + -0.26 = 0

Reorder the terms:
-0.26 + 0.16x + 0.16x2 = 0

Solving
-0.26 + 0.16x + 0.16x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
0.16 the coefficient of the squared term: 

Divide each side by '0.16'.
-1.625 + x + x2 = 0

Move the constant term to the right:

Add '1.625' to each side of the equation.
-1.625 + x + 1.625 + x2 = 0 + 1.625

Reorder the terms:
-1.625 + 1.625 + x + x2 = 0 + 1.625

Combine like terms: -1.625 + 1.625 = 0.000
0.000 + x + x2 = 0 + 1.625
x + x2 = 0 + 1.625

Combine like terms: 0 + 1.625 = 1.625
x + x2 = 1.625

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + x2 = 1.625 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 1.625 + 0.25

Combine like terms: 1.625 + 0.25 = 1.875
1.25 + x2 = 1.875

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 1.875

Calculate the square root of the right side: 1.369306394

Break this problem into two subproblems by setting 
(x + 0.5) equal to 1.369306394 and -1.369306394.

Subproblem 1

x + 0.5 = 1.369306394 Simplifying x + 0.5 = 1.369306394 Reorder the terms: 0.5 + x = 1.369306394 Solving 0.5 + x = 1.369306394 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.369306394 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.369306394 + -0.5 x = 1.369306394 + -0.5 Combine like terms: 1.369306394 + -0.5 = 0.869306394 x = 0.869306394 Simplifying x = 0.869306394

Subproblem 2

x + 0.5 = -1.369306394 Simplifying x + 0.5 = -1.369306394 Reorder the terms: 0.5 + x = -1.369306394 Solving 0.5 + x = -1.369306394 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.369306394 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.369306394 + -0.5 x = -1.369306394 + -0.5 Combine like terms: -1.369306394 + -0.5 = -1.869306394 x = -1.869306394 Simplifying x = -1.869306394

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.869306394, -1.869306394}

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