4x^3-280x^2+4900=4x^3-200x^2+2500x

Solution for 4x^3-280x^2+4900=4x^3-200x^2+2500x equation:

Simplifying
4x3 + -280x2 + 4900 = 4x3 + -200x2 + 2500x

Reorder the terms:
4900 + -280x2 + 4x3 = 4x3 + -200x2 + 2500x

Reorder the terms:
4900 + -280x2 + 4x3 = 2500x + -200x2 + 4x3

Add '-4x3' to each side of the equation.
4900 + -280x2 + 4x3 + -4x3 = 2500x + -200x2 + 4x3 + -4x3

Combine like terms: 4x3 + -4x3 = 0
4900 + -280x2 + 0 = 2500x + -200x2 + 4x3 + -4x3
4900 + -280x2 = 2500x + -200x2 + 4x3 + -4x3

Combine like terms: 4x3 + -4x3 = 0
4900 + -280x2 = 2500x + -200x2 + 0
4900 + -280x2 = 2500x + -200x2

Solving
4900 + -280x2 = 2500x + -200x2

Solving for variable 'x'.

Reorder the terms:
4900 + -2500x + -280x2 + 200x2 = 2500x + -200x2 + -2500x + 200x2

Combine like terms: -280x2 + 200x2 = -80x2
4900 + -2500x + -80x2 = 2500x + -200x2 + -2500x + 200x2

Reorder the terms:
4900 + -2500x + -80x2 = 2500x + -2500x + -200x2 + 200x2

Combine like terms: 2500x + -2500x = 0
4900 + -2500x + -80x2 = 0 + -200x2 + 200x2
4900 + -2500x + -80x2 = -200x2 + 200x2

Combine like terms: -200x2 + 200x2 = 0
4900 + -2500x + -80x2 = 0

Factor out the Greatest Common Factor (GCF), '20'.
20(245 + -125x + -4x2) = 0

Ignore the factor 20.
Subproblem 1
Set the factor '(245 + -125x + -4x2)' equal to zero and attempt to solve:

Simplifying
245 + -125x + -4x2 = 0

Solving
245 + -125x + -4x2 = 0

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

Divide each side by '-4'.
-61.25 + 31.25x + x2 = 0

Move the constant term to the right:

Add '61.25' to each side of the equation.
-61.25 + 31.25x + 61.25 + x2 = 0 + 61.25

Reorder the terms:
-61.25 + 61.25 + 31.25x + x2 = 0 + 61.25

Combine like terms: -61.25 + 61.25 = 0.00
0.00 + 31.25x + x2 = 0 + 61.25
31.25x + x2 = 0 + 61.25

Combine like terms: 0 + 61.25 = 61.25
31.25x + x2 = 61.25

The x term is 31.25x.  Take half its coefficient (15.625).
Square it (244.140625) and add it to both sides.

Add '244.140625' to each side of the equation.
31.25x + 244.140625 + x2 = 61.25 + 244.140625

Reorder the terms:
244.140625 + 31.25x + x2 = 61.25 + 244.140625

Combine like terms: 61.25 + 244.140625 = 305.390625
244.140625 + 31.25x + x2 = 305.390625

Factor a perfect square on the left side:
(x + 15.625)(x + 15.625) = 305.390625

Calculate the square root of the right side: 17.475429179

Break this problem into two subproblems by setting 
(x + 15.625) equal to 17.475429179 and -17.475429179.

Subproblem 1
x + 15.625 = 17.475429179

Simplifying
x + 15.625 = 17.475429179

Reorder the terms:
15.625 + x = 17.475429179

Solving
15.625 + x = 17.475429179

Solving for variable 'x'.

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

Add '-15.625' to each side of the equation.
15.625 + -15.625 + x = 17.475429179 + -15.625

Combine like terms: 15.625 + -15.625 = 0.000
0.000 + x = 17.475429179 + -15.625
x = 17.475429179 + -15.625

Combine like terms: 17.475429179 + -15.625 = 1.850429179
x = 1.850429179

Simplifying
x = 1.850429179

Subproblem 2
x + 15.625 = -17.475429179

Simplifying
x + 15.625 = -17.475429179

Reorder the terms:
15.625 + x = -17.475429179

Solving
15.625 + x = -17.475429179

Solving for variable 'x'.

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

Add '-15.625' to each side of the equation.
15.625 + -15.625 + x = -17.475429179 + -15.625

Combine like terms: 15.625 + -15.625 = 0.000
0.000 + x = -17.475429179 + -15.625
x = -17.475429179 + -15.625

Combine like terms: -17.475429179 + -15.625 = -33.100429179
x = -33.100429179

Simplifying
x = -33.100429179

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.850429179, -33.100429179}
Solution
x = {1.850429179, -33.100429179}