0=35+460x-5x^2

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Solution for 0=35+460x-5x^2 equation: 


Simplifying
0 = 35 + 460x + -5x2

Solving
0 = 35 + 460x + -5x2

Solving for variable 'x'.

Combine like terms: 0 + -35 = -35
-35 + -460x + 5x2 = 35 + 460x + -5x2 + -35 + -460x + 5x2

Reorder the terms:
-35 + -460x + 5x2 = 35 + -35 + 460x + -460x + -5x2 + 5x2

Combine like terms: 35 + -35 = 0
-35 + -460x + 5x2 = 0 + 460x + -460x + -5x2 + 5x2
-35 + -460x + 5x2 = 460x + -460x + -5x2 + 5x2

Combine like terms: 460x + -460x = 0
-35 + -460x + 5x2 = 0 + -5x2 + 5x2
-35 + -460x + 5x2 = -5x2 + 5x2

Combine like terms: -5x2 + 5x2 = 0
-35 + -460x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-7 + -92x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-7 + -92x + x2)' equal to zero and attempt to solve:

Simplifying
-7 + -92x + x2 = 0

Solving
-7 + -92x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -92x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + -92x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -92x + x2 = 0 + 7
-92x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
-92x + x2 = 7

The x term is -92x.  Take half its coefficient (-46).
Square it (2116) and add it to both sides.

Add '2116' to each side of the equation.
-92x + 2116 + x2 = 7 + 2116

Reorder the terms:
2116 + -92x + x2 = 7 + 2116

Combine like terms: 7 + 2116 = 2123
2116 + -92x + x2 = 2123

Factor a perfect square on the left side:
(x + -46)(x + -46) = 2123

Calculate the square root of the right side: 46.076024134

Break this problem into two subproblems by setting 
(x + -46) equal to 46.076024134 and -46.076024134.


Subproblem 1
x + -46 = 46.076024134

Simplifying
x + -46 = 46.076024134

Reorder the terms:
-46 + x = 46.076024134

Solving
-46 + x = 46.076024134

Solving for variable 'x'.

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

Add '46' to each side of the equation.
-46 + 46 + x = 46.076024134 + 46

Combine like terms: -46 + 46 = 0
0 + x = 46.076024134 + 46
x = 46.076024134 + 46

Combine like terms: 46.076024134 + 46 = 92.076024134
x = 92.076024134

Simplifying
x = 92.076024134


Subproblem 2
x + -46 = -46.076024134

Simplifying
x + -46 = -46.076024134

Reorder the terms:
-46 + x = -46.076024134

Solving
-46 + x = -46.076024134

Solving for variable 'x'.

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

Add '46' to each side of the equation.
-46 + 46 + x = -46.076024134 + 46

Combine like terms: -46 + 46 = 0
0 + x = -46.076024134 + 46
x = -46.076024134 + 46

Combine like terms: -46.076024134 + 46 = -0.076024134
x = -0.076024134

Simplifying
x = -0.076024134


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {92.076024134, -0.076024134}
Solution
x = {92.076024134, -0.076024134}

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