40x^2=10000(x-4)

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Solution for 40x^2=10000(x-4) equation:


Simplifying
40x2 = 10000(x + -4)

Reorder the terms:
40x2 = 10000(-4 + x)
40x2 = (-4 * 10000 + x * 10000)
40x2 = (-40000 + 10000x)

Solving
40x2 = -40000 + 10000x

Solving for variable 'x'.

Reorder the terms:
40000 + -10000x + 40x2 = -40000 + 10000x + 40000 + -10000x

Reorder the terms:
40000 + -10000x + 40x2 = -40000 + 40000 + 10000x + -10000x

Combine like terms: -40000 + 40000 = 0
40000 + -10000x + 40x2 = 0 + 10000x + -10000x
40000 + -10000x + 40x2 = 10000x + -10000x

Combine like terms: 10000x + -10000x = 0
40000 + -10000x + 40x2 = 0

Factor out the Greatest Common Factor (GCF), '40'.
40(1000 + -250x + x2) = 0

Ignore the factor 40.

Subproblem 1
Set the factor '(1000 + -250x + x2)' equal to zero and attempt to solve:

Simplifying
1000 + -250x + x2 = 0

Solving
1000 + -250x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1000' to each side of the equation.
1000 + -250x + -1000 + x2 = 0 + -1000

Reorder the terms:
1000 + -1000 + -250x + x2 = 0 + -1000

Combine like terms: 1000 + -1000 = 0
0 + -250x + x2 = 0 + -1000
-250x + x2 = 0 + -1000

Combine like terms: 0 + -1000 = -1000
-250x + x2 = -1000

The x term is -250x.  Take half its coefficient (-125).
Square it (15625) and add it to both sides.

Add '15625' to each side of the equation.
-250x + 15625 + x2 = -1000 + 15625

Reorder the terms:
15625 + -250x + x2 = -1000 + 15625

Combine like terms: -1000 + 15625 = 14625
15625 + -250x + x2 = 14625

Factor a perfect square on the left side:
(x + -125)(x + -125) = 14625

Calculate the square root of the right side: 120.933866224

Break this problem into two subproblems by setting 
(x + -125) equal to 120.933866224 and -120.933866224.


Subproblem 1
x + -125 = 120.933866224

Simplifying
x + -125 = 120.933866224

Reorder the terms:
-125 + x = 120.933866224

Solving
-125 + x = 120.933866224

Solving for variable 'x'.

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

Add '125' to each side of the equation.
-125 + 125 + x = 120.933866224 + 125

Combine like terms: -125 + 125 = 0
0 + x = 120.933866224 + 125
x = 120.933866224 + 125

Combine like terms: 120.933866224 + 125 = 245.933866224
x = 245.933866224

Simplifying
x = 245.933866224


Subproblem 2
x + -125 = -120.933866224

Simplifying
x + -125 = -120.933866224

Reorder the terms:
-125 + x = -120.933866224

Solving
-125 + x = -120.933866224

Solving for variable 'x'.

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

Add '125' to each side of the equation.
-125 + 125 + x = -120.933866224 + 125

Combine like terms: -125 + 125 = 0
0 + x = -120.933866224 + 125
x = -120.933866224 + 125

Combine like terms: -120.933866224 + 125 = 4.066133776
x = 4.066133776

Simplifying
x = 4.066133776


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {245.933866224, 4.066133776}
Solution
x = {245.933866224, 4.066133776}

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