40x^2-1000x+1000=0

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Solution for 40x^2-1000x+1000=0 equation: 


Simplifying
40x2 + -1000x + 1000 = 0

Reorder the terms:
1000 + -1000x + 40x2 = 0

Solving
1000 + -1000x + 40x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '40'.
40(25 + -25x + x2) = 0

Ignore the factor 40.

Subproblem 1
Set the factor '(25 + -25x + x2)' equal to zero and attempt to solve:

Simplifying
25 + -25x + x2 = 0

Solving
25 + -25x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-25' to each side of the equation.
25 + -25x + -25 + x2 = 0 + -25

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

Combine like terms: 25 + -25 = 0
0 + -25x + x2 = 0 + -25
-25x + x2 = 0 + -25

Combine like terms: 0 + -25 = -25
-25x + x2 = -25

The x term is -25x.  Take half its coefficient (-12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
-25x + 156.25 + x2 = -25 + 156.25

Reorder the terms:
156.25 + -25x + x2 = -25 + 156.25

Combine like terms: -25 + 156.25 = 131.25
156.25 + -25x + x2 = 131.25

Factor a perfect square on the left side:
(x + -12.5)(x + -12.5) = 131.25

Calculate the square root of the right side: 11.456439237

Break this problem into two subproblems by setting 
(x + -12.5) equal to 11.456439237 and -11.456439237.


Subproblem 1
x + -12.5 = 11.456439237

Simplifying
x + -12.5 = 11.456439237

Reorder the terms:
-12.5 + x = 11.456439237

Solving
-12.5 + x = 11.456439237

Solving for variable 'x'.

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

Add '12.5' to each side of the equation.
-12.5 + 12.5 + x = 11.456439237 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + x = 11.456439237 + 12.5
x = 11.456439237 + 12.5

Combine like terms: 11.456439237 + 12.5 = 23.956439237
x = 23.956439237

Simplifying
x = 23.956439237


Subproblem 2
x + -12.5 = -11.456439237

Simplifying
x + -12.5 = -11.456439237

Reorder the terms:
-12.5 + x = -11.456439237

Solving
-12.5 + x = -11.456439237

Solving for variable 'x'.

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

Add '12.5' to each side of the equation.
-12.5 + 12.5 + x = -11.456439237 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + x = -11.456439237 + 12.5
x = -11.456439237 + 12.5

Combine like terms: -11.456439237 + 12.5 = 1.043560763
x = 1.043560763

Simplifying
x = 1.043560763


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {23.956439237, 1.043560763}
Solution
x = {23.956439237, 1.043560763}

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