-38x^2+3724x-42150=-25x^2+2350x-26000

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Solution for -38x^2+3724x-42150=-25x^2+2350x-26000 equation: 


Simplifying
-38x2 + 3724x + -42150 = -25x2 + 2350x + -26000

Reorder the terms:
-42150 + 3724x + -38x2 = -25x2 + 2350x + -26000

Reorder the terms:
-42150 + 3724x + -38x2 = -26000 + 2350x + -25x2

Solving
-42150 + 3724x + -38x2 = -26000 + 2350x + -25x2

Solving for variable 'x'.

Reorder the terms:
-42150 + 26000 + 3724x + -2350x + -38x2 + 25x2 = -26000 + 2350x + -25x2 + 26000 + -2350x + 25x2

Combine like terms: -42150 + 26000 = -16150
-16150 + 3724x + -2350x + -38x2 + 25x2 = -26000 + 2350x + -25x2 + 26000 + -2350x + 25x2

Combine like terms: 3724x + -2350x = 1374x
-16150 + 1374x + -38x2 + 25x2 = -26000 + 2350x + -25x2 + 26000 + -2350x + 25x2

Combine like terms: -38x2 + 25x2 = -13x2
-16150 + 1374x + -13x2 = -26000 + 2350x + -25x2 + 26000 + -2350x + 25x2

Reorder the terms:
-16150 + 1374x + -13x2 = -26000 + 26000 + 2350x + -2350x + -25x2 + 25x2

Combine like terms: -26000 + 26000 = 0
-16150 + 1374x + -13x2 = 0 + 2350x + -2350x + -25x2 + 25x2
-16150 + 1374x + -13x2 = 2350x + -2350x + -25x2 + 25x2

Combine like terms: 2350x + -2350x = 0
-16150 + 1374x + -13x2 = 0 + -25x2 + 25x2
-16150 + 1374x + -13x2 = -25x2 + 25x2

Combine like terms: -25x2 + 25x2 = 0
-16150 + 1374x + -13x2 = 0

Begin completing the square.  Divide all terms by
-13 the coefficient of the squared term: 

Divide each side by '-13'.
1242.307692 + -105.6923077x + x2 = 0

Move the constant term to the right:

Add '-1242.307692' to each side of the equation.
1242.307692 + -105.6923077x + -1242.307692 + x2 = 0 + -1242.307692

Reorder the terms:
1242.307692 + -1242.307692 + -105.6923077x + x2 = 0 + -1242.307692

Combine like terms: 1242.307692 + -1242.307692 = 0.000000
0.000000 + -105.6923077x + x2 = 0 + -1242.307692
-105.6923077x + x2 = 0 + -1242.307692

Combine like terms: 0 + -1242.307692 = -1242.307692
-105.6923077x + x2 = -1242.307692

The x term is -105.6923077x.  Take half its coefficient (-52.84615385).
Square it (2792.715977) and add it to both sides.

Add '2792.715977' to each side of the equation.
-105.6923077x + 2792.715977 + x2 = -1242.307692 + 2792.715977

Reorder the terms:
2792.715977 + -105.6923077x + x2 = -1242.307692 + 2792.715977

Combine like terms: -1242.307692 + 2792.715977 = 1550.408285
2792.715977 + -105.6923077x + x2 = 1550.408285

Factor a perfect square on the left side:
(x + -52.84615385)(x + -52.84615385) = 1550.408285

Calculate the square root of the right side: 39.375224253

Break this problem into two subproblems by setting 
(x + -52.84615385) equal to 39.375224253 and -39.375224253.


Subproblem 1
x + -52.84615385 = 39.375224253

Simplifying
x + -52.84615385 = 39.375224253

Reorder the terms:
-52.84615385 + x = 39.375224253

Solving
-52.84615385 + x = 39.375224253

Solving for variable 'x'.

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

Add '52.84615385' to each side of the equation.
-52.84615385 + 52.84615385 + x = 39.375224253 + 52.84615385

Combine like terms: -52.84615385 + 52.84615385 = 0.00000000
0.00000000 + x = 39.375224253 + 52.84615385
x = 39.375224253 + 52.84615385

Combine like terms: 39.375224253 + 52.84615385 = 92.221378103
x = 92.221378103

Simplifying
x = 92.221378103


Subproblem 2
x + -52.84615385 = -39.375224253

Simplifying
x + -52.84615385 = -39.375224253

Reorder the terms:
-52.84615385 + x = -39.375224253

Solving
-52.84615385 + x = -39.375224253

Solving for variable 'x'.

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

Add '52.84615385' to each side of the equation.
-52.84615385 + 52.84615385 + x = -39.375224253 + 52.84615385

Combine like terms: -52.84615385 + 52.84615385 = 0.00000000
0.00000000 + x = -39.375224253 + 52.84615385
x = -39.375224253 + 52.84615385

Combine like terms: -39.375224253 + 52.84615385 = 13.470929597
x = 13.470929597

Simplifying
x = 13.470929597


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {92.221378103, 13.470929597}

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