16x^2+12x-1.76=0

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Solution for 16x^2+12x-1.76=0 equation: 


Simplifying
16x2 + 12x + -1.76 = 0

Reorder the terms:
-1.76 + 12x + 16x2 = 0

Solving
-1.76 + 12x + 16x2 = 0

Solving for variable 'x'.

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

Divide each side by '16'.
-0.11 + 0.75x + x2 = 0

Move the constant term to the right:

Add '0.11' to each side of the equation.
-0.11 + 0.75x + 0.11 + x2 = 0 + 0.11

Reorder the terms:
-0.11 + 0.11 + 0.75x + x2 = 0 + 0.11

Combine like terms: -0.11 + 0.11 = 0.00
0.00 + 0.75x + x2 = 0 + 0.11
0.75x + x2 = 0 + 0.11

Combine like terms: 0 + 0.11 = 0.11
0.75x + x2 = 0.11

The x term is 0.75x.  Take half its coefficient (0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
0.75x + 0.140625 + x2 = 0.11 + 0.140625

Reorder the terms:
0.140625 + 0.75x + x2 = 0.11 + 0.140625

Combine like terms: 0.11 + 0.140625 = 0.250625
0.140625 + 0.75x + x2 = 0.250625

Factor a perfect square on the left side:
(x + 0.375)(x + 0.375) = 0.250625

Calculate the square root of the right side: 0.50062461

Break this problem into two subproblems by setting 
(x + 0.375) equal to 0.50062461 and -0.50062461.


Subproblem 1
x + 0.375 = 0.50062461

Simplifying
x + 0.375 = 0.50062461

Reorder the terms:
0.375 + x = 0.50062461

Solving
0.375 + x = 0.50062461

Solving for variable 'x'.

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

Add '-0.375' to each side of the equation.
0.375 + -0.375 + x = 0.50062461 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + x = 0.50062461 + -0.375
x = 0.50062461 + -0.375

Combine like terms: 0.50062461 + -0.375 = 0.12562461
x = 0.12562461

Simplifying
x = 0.12562461


Subproblem 2
x + 0.375 = -0.50062461

Simplifying
x + 0.375 = -0.50062461

Reorder the terms:
0.375 + x = -0.50062461

Solving
0.375 + x = -0.50062461

Solving for variable 'x'.

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

Add '-0.375' to each side of the equation.
0.375 + -0.375 + x = -0.50062461 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + x = -0.50062461 + -0.375
x = -0.50062461 + -0.375

Combine like terms: -0.50062461 + -0.375 = -0.87562461
x = -0.87562461

Simplifying
x = -0.87562461


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.12562461, -0.87562461}

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