151=235x-16x^2

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Solution for 151=235x-16x^2 equation: 


Simplifying
151 = 235x + -16x2

Solving
151 = 235x + -16x2

Solving for variable 'x'.

Reorder the terms:
151 + -235x + 16x2 = 235x + -235x + -16x2 + 16x2

Combine like terms: 235x + -235x = 0
151 + -235x + 16x2 = 0 + -16x2 + 16x2
151 + -235x + 16x2 = -16x2 + 16x2

Combine like terms: -16x2 + 16x2 = 0
151 + -235x + 16x2 = 0

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

Divide each side by '16'.
9.4375 + -14.6875x + x2 = 0

Move the constant term to the right:

Add '-9.4375' to each side of the equation.
9.4375 + -14.6875x + -9.4375 + x2 = 0 + -9.4375

Reorder the terms:
9.4375 + -9.4375 + -14.6875x + x2 = 0 + -9.4375

Combine like terms: 9.4375 + -9.4375 = 0.0000
0.0000 + -14.6875x + x2 = 0 + -9.4375
-14.6875x + x2 = 0 + -9.4375

Combine like terms: 0 + -9.4375 = -9.4375
-14.6875x + x2 = -9.4375

The x term is -14.6875x.  Take half its coefficient (-7.34375).
Square it (53.93066406) and add it to both sides.

Add '53.93066406' to each side of the equation.
-14.6875x + 53.93066406 + x2 = -9.4375 + 53.93066406

Reorder the terms:
53.93066406 + -14.6875x + x2 = -9.4375 + 53.93066406

Combine like terms: -9.4375 + 53.93066406 = 44.49316406
53.93066406 + -14.6875x + x2 = 44.49316406

Factor a perfect square on the left side:
(x + -7.34375)(x + -7.34375) = 44.49316406

Calculate the square root of the right side: 6.670319637

Break this problem into two subproblems by setting 
(x + -7.34375) equal to 6.670319637 and -6.670319637.


Subproblem 1
x + -7.34375 = 6.670319637

Simplifying
x + -7.34375 = 6.670319637

Reorder the terms:
-7.34375 + x = 6.670319637

Solving
-7.34375 + x = 6.670319637

Solving for variable 'x'.

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

Add '7.34375' to each side of the equation.
-7.34375 + 7.34375 + x = 6.670319637 + 7.34375

Combine like terms: -7.34375 + 7.34375 = 0.00000
0.00000 + x = 6.670319637 + 7.34375
x = 6.670319637 + 7.34375

Combine like terms: 6.670319637 + 7.34375 = 14.014069637
x = 14.014069637

Simplifying
x = 14.014069637


Subproblem 2
x + -7.34375 = -6.670319637

Simplifying
x + -7.34375 = -6.670319637

Reorder the terms:
-7.34375 + x = -6.670319637

Solving
-7.34375 + x = -6.670319637

Solving for variable 'x'.

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

Add '7.34375' to each side of the equation.
-7.34375 + 7.34375 + x = -6.670319637 + 7.34375

Combine like terms: -7.34375 + 7.34375 = 0.00000
0.00000 + x = -6.670319637 + 7.34375
x = -6.670319637 + 7.34375

Combine like terms: -6.670319637 + 7.34375 = 0.673430363
x = 0.673430363

Simplifying
x = 0.673430363


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.014069637, 0.673430363}

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