(x^2-14x+49)5=90

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Solution for (x^2-14x+49)5=90 equation: 


Simplifying
(x2 + -14x + 49) * 5 = 90

Reorder the terms:
(49 + -14x + x2) * 5 = 90

Reorder the terms for easier multiplication:
5(49 + -14x + x2) = 90
(49 * 5 + -14x * 5 + x2 * 5) = 90
(245 + -70x + 5x2) = 90

Solving
245 + -70x + 5x2 = 90

Solving for variable 'x'.

Reorder the terms:
245 + -90 + -70x + 5x2 = 90 + -90

Combine like terms: 245 + -90 = 155
155 + -70x + 5x2 = 90 + -90

Combine like terms: 90 + -90 = 0
155 + -70x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(31 + -14x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(31 + -14x + x2)' equal to zero and attempt to solve:

Simplifying
31 + -14x + x2 = 0

Solving
31 + -14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-31' to each side of the equation.
31 + -14x + -31 + x2 = 0 + -31

Reorder the terms:
31 + -31 + -14x + x2 = 0 + -31

Combine like terms: 31 + -31 = 0
0 + -14x + x2 = 0 + -31
-14x + x2 = 0 + -31

Combine like terms: 0 + -31 = -31
-14x + x2 = -31

The x term is -14x.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14x + 49 + x2 = -31 + 49

Reorder the terms:
49 + -14x + x2 = -31 + 49

Combine like terms: -31 + 49 = 18
49 + -14x + x2 = 18

Factor a perfect square on the left side:
(x + -7)(x + -7) = 18

Calculate the square root of the right side: 4.242640687

Break this problem into two subproblems by setting 
(x + -7) equal to 4.242640687 and -4.242640687.


Subproblem 1
x + -7 = 4.242640687

Simplifying
x + -7 = 4.242640687

Reorder the terms:
-7 + x = 4.242640687

Solving
-7 + x = 4.242640687

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = 4.242640687 + 7

Combine like terms: -7 + 7 = 0
0 + x = 4.242640687 + 7
x = 4.242640687 + 7

Combine like terms: 4.242640687 + 7 = 11.242640687
x = 11.242640687

Simplifying
x = 11.242640687


Subproblem 2
x + -7 = -4.242640687

Simplifying
x + -7 = -4.242640687

Reorder the terms:
-7 + x = -4.242640687

Solving
-7 + x = -4.242640687

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = -4.242640687 + 7

Combine like terms: -7 + 7 = 0
0 + x = -4.242640687 + 7
x = -4.242640687 + 7

Combine like terms: -4.242640687 + 7 = 2.757359313
x = 2.757359313

Simplifying
x = 2.757359313


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.242640687, 2.757359313}
Solution
x = {11.242640687, 2.757359313}

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