4x^2-64x+305=x^2+24x+144

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Solution for 4x^2-64x+305=x^2+24x+144 equation: 


Simplifying
4x2 + -64x + 305 = x2 + 24x + 144

Reorder the terms:
305 + -64x + 4x2 = x2 + 24x + 144

Reorder the terms:
305 + -64x + 4x2 = 144 + 24x + x2

Solving
305 + -64x + 4x2 = 144 + 24x + x2

Solving for variable 'x'.

Reorder the terms:
305 + -144 + -64x + -24x + 4x2 + -1x2 = 144 + 24x + x2 + -144 + -24x + -1x2

Combine like terms: 305 + -144 = 161
161 + -64x + -24x + 4x2 + -1x2 = 144 + 24x + x2 + -144 + -24x + -1x2

Combine like terms: -64x + -24x = -88x
161 + -88x + 4x2 + -1x2 = 144 + 24x + x2 + -144 + -24x + -1x2

Combine like terms: 4x2 + -1x2 = 3x2
161 + -88x + 3x2 = 144 + 24x + x2 + -144 + -24x + -1x2

Reorder the terms:
161 + -88x + 3x2 = 144 + -144 + 24x + -24x + x2 + -1x2

Combine like terms: 144 + -144 = 0
161 + -88x + 3x2 = 0 + 24x + -24x + x2 + -1x2
161 + -88x + 3x2 = 24x + -24x + x2 + -1x2

Combine like terms: 24x + -24x = 0
161 + -88x + 3x2 = 0 + x2 + -1x2
161 + -88x + 3x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
161 + -88x + 3x2 = 0

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

Divide each side by '3'.
53.66666667 + -29.33333333x + x2 = 0

Move the constant term to the right:

Add '-53.66666667' to each side of the equation.
53.66666667 + -29.33333333x + -53.66666667 + x2 = 0 + -53.66666667

Reorder the terms:
53.66666667 + -53.66666667 + -29.33333333x + x2 = 0 + -53.66666667

Combine like terms: 53.66666667 + -53.66666667 = 0.00000000
0.00000000 + -29.33333333x + x2 = 0 + -53.66666667
-29.33333333x + x2 = 0 + -53.66666667

Combine like terms: 0 + -53.66666667 = -53.66666667
-29.33333333x + x2 = -53.66666667

The x term is -29.33333333x.  Take half its coefficient (-14.66666667).
Square it (215.1111112) and add it to both sides.

Add '215.1111112' to each side of the equation.
-29.33333333x + 215.1111112 + x2 = -53.66666667 + 215.1111112

Reorder the terms:
215.1111112 + -29.33333333x + x2 = -53.66666667 + 215.1111112

Combine like terms: -53.66666667 + 215.1111112 = 161.44444453
215.1111112 + -29.33333333x + x2 = 161.44444453

Factor a perfect square on the left side:
(x + -14.66666667)(x + -14.66666667) = 161.44444453

Calculate the square root of the right side: 12.706079038

Break this problem into two subproblems by setting 
(x + -14.66666667) equal to 12.706079038 and -12.706079038.


Subproblem 1
x + -14.66666667 = 12.706079038

Simplifying
x + -14.66666667 = 12.706079038

Reorder the terms:
-14.66666667 + x = 12.706079038

Solving
-14.66666667 + x = 12.706079038

Solving for variable 'x'.

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

Add '14.66666667' to each side of the equation.
-14.66666667 + 14.66666667 + x = 12.706079038 + 14.66666667

Combine like terms: -14.66666667 + 14.66666667 = 0.00000000
0.00000000 + x = 12.706079038 + 14.66666667
x = 12.706079038 + 14.66666667

Combine like terms: 12.706079038 + 14.66666667 = 27.372745708
x = 27.372745708

Simplifying
x = 27.372745708


Subproblem 2
x + -14.66666667 = -12.706079038

Simplifying
x + -14.66666667 = -12.706079038

Reorder the terms:
-14.66666667 + x = -12.706079038

Solving
-14.66666667 + x = -12.706079038

Solving for variable 'x'.

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

Add '14.66666667' to each side of the equation.
-14.66666667 + 14.66666667 + x = -12.706079038 + 14.66666667

Combine like terms: -14.66666667 + 14.66666667 = 0.00000000
0.00000000 + x = -12.706079038 + 14.66666667
x = -12.706079038 + 14.66666667

Combine like terms: -12.706079038 + 14.66666667 = 1.960587632
x = 1.960587632

Simplifying
x = 1.960587632


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {27.372745708, 1.960587632}

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