4x^2-30x+32=0

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Solution for 4x^2-30x+32=0 equation: 


Simplifying
4x2 + -30x + 32 = 0

Reorder the terms:
32 + -30x + 4x2 = 0

Solving
32 + -30x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(16 + -15x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(16 + -15x + 2x2)' equal to zero and attempt to solve:

Simplifying
16 + -15x + 2x2 = 0

Solving
16 + -15x + 2x2 = 0

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

Divide each side by '2'.
8 + -7.5x + x2 = 0

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + -7.5x + -8 + x2 = 0 + -8

Reorder the terms:
8 + -8 + -7.5x + x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -7.5x + x2 = 0 + -8
-7.5x + x2 = 0 + -8

Combine like terms: 0 + -8 = -8
-7.5x + x2 = -8

The x term is -7.5x.  Take half its coefficient (-3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
-7.5x + 14.0625 + x2 = -8 + 14.0625

Reorder the terms:
14.0625 + -7.5x + x2 = -8 + 14.0625

Combine like terms: -8 + 14.0625 = 6.0625
14.0625 + -7.5x + x2 = 6.0625

Factor a perfect square on the left side:
(x + -3.75)(x + -3.75) = 6.0625

Calculate the square root of the right side: 2.46221445

Break this problem into two subproblems by setting 
(x + -3.75) equal to 2.46221445 and -2.46221445.


Subproblem 1
x + -3.75 = 2.46221445

Simplifying
x + -3.75 = 2.46221445

Reorder the terms:
-3.75 + x = 2.46221445

Solving
-3.75 + x = 2.46221445

Solving for variable 'x'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + x = 2.46221445 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + x = 2.46221445 + 3.75
x = 2.46221445 + 3.75

Combine like terms: 2.46221445 + 3.75 = 6.21221445
x = 6.21221445

Simplifying
x = 6.21221445


Subproblem 2
x + -3.75 = -2.46221445

Simplifying
x + -3.75 = -2.46221445

Reorder the terms:
-3.75 + x = -2.46221445

Solving
-3.75 + x = -2.46221445

Solving for variable 'x'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + x = -2.46221445 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + x = -2.46221445 + 3.75
x = -2.46221445 + 3.75

Combine like terms: -2.46221445 + 3.75 = 1.28778555
x = 1.28778555

Simplifying
x = 1.28778555


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.21221445, 1.28778555}
Solution
x = {6.21221445, 1.28778555}

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