-16x^2+234x-13=

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Solution for -16x^2+234x-13= equation: 


Simplifying
-16x2 + 234x + -13 = 0

Reorder the terms:
-13 + 234x + -16x2 = 0

Solving
-13 + 234x + -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'.
0.8125 + -14.625x + x2 = 0

Move the constant term to the right:

Add '-0.8125' to each side of the equation.
0.8125 + -14.625x + -0.8125 + x2 = 0 + -0.8125

Reorder the terms:
0.8125 + -0.8125 + -14.625x + x2 = 0 + -0.8125

Combine like terms: 0.8125 + -0.8125 = 0.0000
0.0000 + -14.625x + x2 = 0 + -0.8125
-14.625x + x2 = 0 + -0.8125

Combine like terms: 0 + -0.8125 = -0.8125
-14.625x + x2 = -0.8125

The x term is -14.625x.  Take half its coefficient (-7.3125).
Square it (53.47265625) and add it to both sides.

Add '53.47265625' to each side of the equation.
-14.625x + 53.47265625 + x2 = -0.8125 + 53.47265625

Reorder the terms:
53.47265625 + -14.625x + x2 = -0.8125 + 53.47265625

Combine like terms: -0.8125 + 53.47265625 = 52.66015625
53.47265625 + -14.625x + x2 = 52.66015625

Factor a perfect square on the left side:
(x + -7.3125)(x + -7.3125) = 52.66015625

Calculate the square root of the right side: 7.256731788

Break this problem into two subproblems by setting 
(x + -7.3125) equal to 7.256731788 and -7.256731788.


Subproblem 1
x + -7.3125 = 7.256731788

Simplifying
x + -7.3125 = 7.256731788

Reorder the terms:
-7.3125 + x = 7.256731788

Solving
-7.3125 + x = 7.256731788

Solving for variable 'x'.

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

Add '7.3125' to each side of the equation.
-7.3125 + 7.3125 + x = 7.256731788 + 7.3125

Combine like terms: -7.3125 + 7.3125 = 0.0000
0.0000 + x = 7.256731788 + 7.3125
x = 7.256731788 + 7.3125

Combine like terms: 7.256731788 + 7.3125 = 14.569231788
x = 14.569231788

Simplifying
x = 14.569231788


Subproblem 2
x + -7.3125 = -7.256731788

Simplifying
x + -7.3125 = -7.256731788

Reorder the terms:
-7.3125 + x = -7.256731788

Solving
-7.3125 + x = -7.256731788

Solving for variable 'x'.

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

Add '7.3125' to each side of the equation.
-7.3125 + 7.3125 + x = -7.256731788 + 7.3125

Combine like terms: -7.3125 + 7.3125 = 0.0000
0.0000 + x = -7.256731788 + 7.3125
x = -7.256731788 + 7.3125

Combine like terms: -7.256731788 + 7.3125 = 0.055768212
x = 0.055768212

Simplifying
x = 0.055768212


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.569231788, 0.055768212}

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