4x-1+18x=16(x-3)(x-4)

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Solution for 4x-1+18x=16(x-3)(x-4) equation:


Simplifying
4x + -1 + 18x = 16(x + -3)(x + -4)

Reorder the terms:
-1 + 4x + 18x = 16(x + -3)(x + -4)

Combine like terms: 4x + 18x = 22x
-1 + 22x = 16(x + -3)(x + -4)

Reorder the terms:
-1 + 22x = 16(-3 + x)(x + -4)

Reorder the terms:
-1 + 22x = 16(-3 + x)(-4 + x)

Multiply (-3 + x) * (-4 + x)
-1 + 22x = 16(-3(-4 + x) + x(-4 + x))
-1 + 22x = 16((-4 * -3 + x * -3) + x(-4 + x))
-1 + 22x = 16((12 + -3x) + x(-4 + x))
-1 + 22x = 16(12 + -3x + (-4 * x + x * x))
-1 + 22x = 16(12 + -3x + (-4x + x2))

Combine like terms: -3x + -4x = -7x
-1 + 22x = 16(12 + -7x + x2)
-1 + 22x = (12 * 16 + -7x * 16 + x2 * 16)
-1 + 22x = (192 + -112x + 16x2)

Solving
-1 + 22x = 192 + -112x + 16x2

Solving for variable 'x'.

Reorder the terms:
-1 + -192 + 22x + 112x + -16x2 = 192 + -112x + 16x2 + -192 + 112x + -16x2

Combine like terms: -1 + -192 = -193
-193 + 22x + 112x + -16x2 = 192 + -112x + 16x2 + -192 + 112x + -16x2

Combine like terms: 22x + 112x = 134x
-193 + 134x + -16x2 = 192 + -112x + 16x2 + -192 + 112x + -16x2

Reorder the terms:
-193 + 134x + -16x2 = 192 + -192 + -112x + 112x + 16x2 + -16x2

Combine like terms: 192 + -192 = 0
-193 + 134x + -16x2 = 0 + -112x + 112x + 16x2 + -16x2
-193 + 134x + -16x2 = -112x + 112x + 16x2 + -16x2

Combine like terms: -112x + 112x = 0
-193 + 134x + -16x2 = 0 + 16x2 + -16x2
-193 + 134x + -16x2 = 16x2 + -16x2

Combine like terms: 16x2 + -16x2 = 0
-193 + 134x + -16x2 = 0

Begin completing the square.  Divide all terms by
-16 the coefficient of the squared term: 

Divide each side by '-16'.
12.0625 + -8.375x + x2 = 0

Move the constant term to the right:

Add '-12.0625' to each side of the equation.
12.0625 + -8.375x + -12.0625 + x2 = 0 + -12.0625

Reorder the terms:
12.0625 + -12.0625 + -8.375x + x2 = 0 + -12.0625

Combine like terms: 12.0625 + -12.0625 = 0.0000
0.0000 + -8.375x + x2 = 0 + -12.0625
-8.375x + x2 = 0 + -12.0625

Combine like terms: 0 + -12.0625 = -12.0625
-8.375x + x2 = -12.0625

The x term is -8.375x.  Take half its coefficient (-4.1875).
Square it (17.53515625) and add it to both sides.

Add '17.53515625' to each side of the equation.
-8.375x + 17.53515625 + x2 = -12.0625 + 17.53515625

Reorder the terms:
17.53515625 + -8.375x + x2 = -12.0625 + 17.53515625

Combine like terms: -12.0625 + 17.53515625 = 5.47265625
17.53515625 + -8.375x + x2 = 5.47265625

Factor a perfect square on the left side:
(x + -4.1875)(x + -4.1875) = 5.47265625

Calculate the square root of the right side: 2.339370909

Break this problem into two subproblems by setting 
(x + -4.1875) equal to 2.339370909 and -2.339370909.


Subproblem 1
x + -4.1875 = 2.339370909

Simplifying
x + -4.1875 = 2.339370909

Reorder the terms:
-4.1875 + x = 2.339370909

Solving
-4.1875 + x = 2.339370909

Solving for variable 'x'.

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

Add '4.1875' to each side of the equation.
-4.1875 + 4.1875 + x = 2.339370909 + 4.1875

Combine like terms: -4.1875 + 4.1875 = 0.0000
0.0000 + x = 2.339370909 + 4.1875
x = 2.339370909 + 4.1875

Combine like terms: 2.339370909 + 4.1875 = 6.526870909
x = 6.526870909

Simplifying
x = 6.526870909


Subproblem 2
x + -4.1875 = -2.339370909

Simplifying
x + -4.1875 = -2.339370909

Reorder the terms:
-4.1875 + x = -2.339370909

Solving
-4.1875 + x = -2.339370909

Solving for variable 'x'.

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

Add '4.1875' to each side of the equation.
-4.1875 + 4.1875 + x = -2.339370909 + 4.1875

Combine like terms: -4.1875 + 4.1875 = 0.0000
0.0000 + x = -2.339370909 + 4.1875
x = -2.339370909 + 4.1875

Combine like terms: -2.339370909 + 4.1875 = 1.848129091
x = 1.848129091

Simplifying
x = 1.848129091


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.526870909, 1.848129091}

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