4x(x-7)+13=27

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Solution for 4x(x-7)+13=27 equation: 


Simplifying
4x(x + -7) + 13 = 27

Reorder the terms:
4x(-7 + x) + 13 = 27
(-7 * 4x + x * 4x) + 13 = 27
(-28x + 4x2) + 13 = 27

Reorder the terms:
13 + -28x + 4x2 = 27

Solving
13 + -28x + 4x2 = 27

Solving for variable 'x'.

Reorder the terms:
13 + -27 + -28x + 4x2 = 27 + -27

Combine like terms: 13 + -27 = -14
-14 + -28x + 4x2 = 27 + -27

Combine like terms: 27 + -27 = 0
-14 + -28x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + -14x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-7 + -14x + 2x2)' equal to zero and attempt to solve:

Simplifying
-7 + -14x + 2x2 = 0

Solving
-7 + -14x + 2x2 = 0

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

Divide each side by '2'.
-3.5 + -7x + x2 = 0

Move the constant term to the right:

Add '3.5' to each side of the equation.
-3.5 + -7x + 3.5 + x2 = 0 + 3.5

Reorder the terms:
-3.5 + 3.5 + -7x + x2 = 0 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + -7x + x2 = 0 + 3.5
-7x + x2 = 0 + 3.5

Combine like terms: 0 + 3.5 = 3.5
-7x + x2 = 3.5

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = 3.5 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 3.5 + 12.25

Combine like terms: 3.5 + 12.25 = 15.75
12.25 + -7x + x2 = 15.75

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 15.75

Calculate the square root of the right side: 3.968626967

Break this problem into two subproblems by setting 
(x + -3.5) equal to 3.968626967 and -3.968626967.


Subproblem 1
x + -3.5 = 3.968626967

Simplifying
x + -3.5 = 3.968626967

Reorder the terms:
-3.5 + x = 3.968626967

Solving
-3.5 + x = 3.968626967

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = 3.968626967 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 3.968626967 + 3.5
x = 3.968626967 + 3.5

Combine like terms: 3.968626967 + 3.5 = 7.468626967
x = 7.468626967

Simplifying
x = 7.468626967


Subproblem 2
x + -3.5 = -3.968626967

Simplifying
x + -3.5 = -3.968626967

Reorder the terms:
-3.5 + x = -3.968626967

Solving
-3.5 + x = -3.968626967

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = -3.968626967 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -3.968626967 + 3.5
x = -3.968626967 + 3.5

Combine like terms: -3.968626967 + 3.5 = -0.468626967
x = -0.468626967

Simplifying
x = -0.468626967


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.468626967, -0.468626967}
Solution
x = {7.468626967, -0.468626967}

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