0=x^2+.151x-0.064

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Solution for 0=x^2+.151x-0.064 equation:


Simplifying
0 = x2 + 0.151x + -0.064

Reorder the terms:
0 = -0.064 + 0.151x + x2

Solving
0 = -0.064 + 0.151x + x2

Solving for variable 'x'.

Combine like terms: 0 + 0.064 = 0.064
0.064 + -0.151x + -1x2 = -0.064 + 0.151x + x2 + 0.064 + -0.151x + -1x2

Reorder the terms:
0.064 + -0.151x + -1x2 = -0.064 + 0.064 + 0.151x + -0.151x + x2 + -1x2

Combine like terms: -0.064 + 0.064 = 0.000
0.064 + -0.151x + -1x2 = 0.000 + 0.151x + -0.151x + x2 + -1x2
0.064 + -0.151x + -1x2 = 0.151x + -0.151x + x2 + -1x2

Combine like terms: 0.151x + -0.151x = 0.000
0.064 + -0.151x + -1x2 = 0.000 + x2 + -1x2
0.064 + -0.151x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
0.064 + -0.151x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-0.064 + 0.151x + x2 = 0

Move the constant term to the right:

Add '0.064' to each side of the equation.
-0.064 + 0.151x + 0.064 + x2 = 0 + 0.064

Reorder the terms:
-0.064 + 0.064 + 0.151x + x2 = 0 + 0.064

Combine like terms: -0.064 + 0.064 = 0.000
0.000 + 0.151x + x2 = 0 + 0.064
0.151x + x2 = 0 + 0.064

Combine like terms: 0 + 0.064 = 0.064
0.151x + x2 = 0.064

The x term is 0.151x.  Take half its coefficient (0.0755).
Square it (0.00570025) and add it to both sides.

Add '0.00570025' to each side of the equation.
0.151x + 0.00570025 + x2 = 0.064 + 0.00570025

Reorder the terms:
0.00570025 + 0.151x + x2 = 0.064 + 0.00570025

Combine like terms: 0.064 + 0.00570025 = 0.06970025
0.00570025 + 0.151x + x2 = 0.06970025

Factor a perfect square on the left side:
(x + 0.0755)(x + 0.0755) = 0.06970025

Calculate the square root of the right side: 0.264008049

Break this problem into two subproblems by setting 
(x + 0.0755) equal to 0.264008049 and -0.264008049.

Subproblem 1

x + 0.0755 = 0.264008049 Simplifying x + 0.0755 = 0.264008049 Reorder the terms: 0.0755 + x = 0.264008049 Solving 0.0755 + x = 0.264008049 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0755' to each side of the equation. 0.0755 + -0.0755 + x = 0.264008049 + -0.0755 Combine like terms: 0.0755 + -0.0755 = 0.0000 0.0000 + x = 0.264008049 + -0.0755 x = 0.264008049 + -0.0755 Combine like terms: 0.264008049 + -0.0755 = 0.188508049 x = 0.188508049 Simplifying x = 0.188508049

Subproblem 2

x + 0.0755 = -0.264008049 Simplifying x + 0.0755 = -0.264008049 Reorder the terms: 0.0755 + x = -0.264008049 Solving 0.0755 + x = -0.264008049 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0755' to each side of the equation. 0.0755 + -0.0755 + x = -0.264008049 + -0.0755 Combine like terms: 0.0755 + -0.0755 = 0.0000 0.0000 + x = -0.264008049 + -0.0755 x = -0.264008049 + -0.0755 Combine like terms: -0.264008049 + -0.0755 = -0.339508049 x = -0.339508049 Simplifying x = -0.339508049

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.188508049, -0.339508049}

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