(4x^2)-42x+63=0

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Solution for (4x^2)-42x+63=0 equation: 


Simplifying
(4x2) + -42x + 63 = 0

Reorder the terms:
63 + -42x + (4x2) = 0

Solving
63 + -42x + (4x2) = 0

Solving for variable 'x'.

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

Divide each side by '4'.
15.75 + -10.5x + x2 = 0

Move the constant term to the right:

Add '-15.75' to each side of the equation.
15.75 + -10.5x + -15.75 + x2 = 0 + -15.75

Reorder the terms:
15.75 + -15.75 + -10.5x + x2 = 0 + -15.75

Combine like terms: 15.75 + -15.75 = 0.00
0.00 + -10.5x + x2 = 0 + -15.75
-10.5x + x2 = 0 + -15.75

Combine like terms: 0 + -15.75 = -15.75
-10.5x + x2 = -15.75

The x term is -10.5x.  Take half its coefficient (-5.25).
Square it (27.5625) and add it to both sides.

Add '27.5625' to each side of the equation.
-10.5x + 27.5625 + x2 = -15.75 + 27.5625

Reorder the terms:
27.5625 + -10.5x + x2 = -15.75 + 27.5625

Combine like terms: -15.75 + 27.5625 = 11.8125
27.5625 + -10.5x + x2 = 11.8125

Factor a perfect square on the left side:
((x) + -5.25)((x) + -5.25) = 11.8125

Calculate the square root of the right side: 3.436931771

Break this problem into two subproblems by setting 
((x) + -5.25) equal to 3.436931771 and -3.436931771.


Subproblem 1
(x) + -5.25 = 3.436931771

Simplifying
(x) + -5.25 = 3.436931771
x + -5.25 = 3.436931771

Reorder the terms:
-5.25 + x = 3.436931771

Solving
-5.25 + x = 3.436931771

Solving for variable 'x'.

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

Add '5.25' to each side of the equation.
-5.25 + 5.25 + x = 3.436931771 + 5.25

Combine like terms: -5.25 + 5.25 = 0.00
0.00 + x = 3.436931771 + 5.25
x = 3.436931771 + 5.25

Combine like terms: 3.436931771 + 5.25 = 8.686931771
x = 8.686931771

Simplifying
x = 8.686931771


Subproblem 2
(x) + -5.25 = -3.436931771

Simplifying
(x) + -5.25 = -3.436931771
x + -5.25 = -3.436931771

Reorder the terms:
-5.25 + x = -3.436931771

Solving
-5.25 + x = -3.436931771

Solving for variable 'x'.

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

Add '5.25' to each side of the equation.
-5.25 + 5.25 + x = -3.436931771 + 5.25

Combine like terms: -5.25 + 5.25 = 0.00
0.00 + x = -3.436931771 + 5.25
x = -3.436931771 + 5.25

Combine like terms: -3.436931771 + 5.25 = 1.813068229
x = 1.813068229

Simplifying
x = 1.813068229


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.686931771, 1.813068229}

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