32x^2+28x-7=0

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Solution for 32x^2+28x-7=0 equation: 


Simplifying
32x2 + 28x + -7 = 0

Reorder the terms:
-7 + 28x + 32x2 = 0

Solving
-7 + 28x + 32x2 = 0

Solving for variable 'x'.

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

Divide each side by '32'.
-0.21875 + 0.875x + x2 = 0

Move the constant term to the right:

Add '0.21875' to each side of the equation.
-0.21875 + 0.875x + 0.21875 + x2 = 0 + 0.21875

Reorder the terms:
-0.21875 + 0.21875 + 0.875x + x2 = 0 + 0.21875

Combine like terms: -0.21875 + 0.21875 = 0.00000
0.00000 + 0.875x + x2 = 0 + 0.21875
0.875x + x2 = 0 + 0.21875

Combine like terms: 0 + 0.21875 = 0.21875
0.875x + x2 = 0.21875

The x term is 0.875x.  Take half its coefficient (0.4375).
Square it (0.19140625) and add it to both sides.

Add '0.19140625' to each side of the equation.
0.875x + 0.19140625 + x2 = 0.21875 + 0.19140625

Reorder the terms:
0.19140625 + 0.875x + x2 = 0.21875 + 0.19140625

Combine like terms: 0.21875 + 0.19140625 = 0.41015625
0.19140625 + 0.875x + x2 = 0.41015625

Factor a perfect square on the left side:
(x + 0.4375)(x + 0.4375) = 0.41015625

Calculate the square root of the right side: 0.640434423

Break this problem into two subproblems by setting 
(x + 0.4375) equal to 0.640434423 and -0.640434423.


Subproblem 1
x + 0.4375 = 0.640434423

Simplifying
x + 0.4375 = 0.640434423

Reorder the terms:
0.4375 + x = 0.640434423

Solving
0.4375 + x = 0.640434423

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.4375' to each side of the equation.
0.4375 + -0.4375 + x = 0.640434423 + -0.4375

Combine like terms: 0.4375 + -0.4375 = 0.0000
0.0000 + x = 0.640434423 + -0.4375
x = 0.640434423 + -0.4375

Combine like terms: 0.640434423 + -0.4375 = 0.202934423
x = 0.202934423

Simplifying
x = 0.202934423


Subproblem 2
x + 0.4375 = -0.640434423

Simplifying
x + 0.4375 = -0.640434423

Reorder the terms:
0.4375 + x = -0.640434423

Solving
0.4375 + x = -0.640434423

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.4375' to each side of the equation.
0.4375 + -0.4375 + x = -0.640434423 + -0.4375

Combine like terms: 0.4375 + -0.4375 = 0.0000
0.0000 + x = -0.640434423 + -0.4375
x = -0.640434423 + -0.4375

Combine like terms: -0.640434423 + -0.4375 = -1.077934423
x = -1.077934423

Simplifying
x = -1.077934423


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.202934423, -1.077934423}

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