20x^2+25x-1000=0

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Solution for 20x^2+25x-1000=0 equation: 


Simplifying
20x2 + 25x + -1000 = 0

Reorder the terms:
-1000 + 25x + 20x2 = 0

Solving
-1000 + 25x + 20x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-200 + 5x + 4x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-200 + 5x + 4x2)' equal to zero and attempt to solve:

Simplifying
-200 + 5x + 4x2 = 0

Solving
-200 + 5x + 4x2 = 0

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

Divide each side by '4'.
-50 + 1.25x + x2 = 0

Move the constant term to the right:

Add '50' to each side of the equation.
-50 + 1.25x + 50 + x2 = 0 + 50

Reorder the terms:
-50 + 50 + 1.25x + x2 = 0 + 50

Combine like terms: -50 + 50 = 0
0 + 1.25x + x2 = 0 + 50
1.25x + x2 = 0 + 50

Combine like terms: 0 + 50 = 50
1.25x + x2 = 50

The x term is 1.25x.  Take half its coefficient (0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
1.25x + 0.390625 + x2 = 50 + 0.390625

Reorder the terms:
0.390625 + 1.25x + x2 = 50 + 0.390625

Combine like terms: 50 + 0.390625 = 50.390625
0.390625 + 1.25x + x2 = 50.390625

Factor a perfect square on the left side:
(x + 0.625)(x + 0.625) = 50.390625

Calculate the square root of the right side: 7.098635432

Break this problem into two subproblems by setting 
(x + 0.625) equal to 7.098635432 and -7.098635432.


Subproblem 1
x + 0.625 = 7.098635432

Simplifying
x + 0.625 = 7.098635432

Reorder the terms:
0.625 + x = 7.098635432

Solving
0.625 + x = 7.098635432

Solving for variable 'x'.

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

Add '-0.625' to each side of the equation.
0.625 + -0.625 + x = 7.098635432 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + x = 7.098635432 + -0.625
x = 7.098635432 + -0.625

Combine like terms: 7.098635432 + -0.625 = 6.473635432
x = 6.473635432

Simplifying
x = 6.473635432


Subproblem 2
x + 0.625 = -7.098635432

Simplifying
x + 0.625 = -7.098635432

Reorder the terms:
0.625 + x = -7.098635432

Solving
0.625 + x = -7.098635432

Solving for variable 'x'.

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

Add '-0.625' to each side of the equation.
0.625 + -0.625 + x = -7.098635432 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + x = -7.098635432 + -0.625
x = -7.098635432 + -0.625

Combine like terms: -7.098635432 + -0.625 = -7.723635432
x = -7.723635432

Simplifying
x = -7.723635432


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.473635432, -7.723635432}
Solution
x = {6.473635432, -7.723635432}

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