50x^2+40x-1000=0

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Solution for 50x^2+40x-1000=0 equation: 


Simplifying
50x2 + 40x + -1000 = 0

Reorder the terms:
-1000 + 40x + 50x2 = 0

Solving
-1000 + 40x + 50x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10'.
10(-100 + 4x + 5x2) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(-100 + 4x + 5x2)' equal to zero and attempt to solve:

Simplifying
-100 + 4x + 5x2 = 0

Solving
-100 + 4x + 5x2 = 0

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

Divide each side by '5'.
-20 + 0.8x + x2 = 0

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + 0.8x + 20 + x2 = 0 + 20

Reorder the terms:
-20 + 20 + 0.8x + x2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + 0.8x + x2 = 0 + 20
0.8x + x2 = 0 + 20

Combine like terms: 0 + 20 = 20
0.8x + x2 = 20

The x term is 0.8x.  Take half its coefficient (0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
0.8x + 0.16 + x2 = 20 + 0.16

Reorder the terms:
0.16 + 0.8x + x2 = 20 + 0.16

Combine like terms: 20 + 0.16 = 20.16
0.16 + 0.8x + x2 = 20.16

Factor a perfect square on the left side:
(x + 0.4)(x + 0.4) = 20.16

Calculate the square root of the right side: 4.489988864

Break this problem into two subproblems by setting 
(x + 0.4) equal to 4.489988864 and -4.489988864.


Subproblem 1
x + 0.4 = 4.489988864

Simplifying
x + 0.4 = 4.489988864

Reorder the terms:
0.4 + x = 4.489988864

Solving
0.4 + x = 4.489988864

Solving for variable 'x'.

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

Add '-0.4' to each side of the equation.
0.4 + -0.4 + x = 4.489988864 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + x = 4.489988864 + -0.4
x = 4.489988864 + -0.4

Combine like terms: 4.489988864 + -0.4 = 4.089988864
x = 4.089988864

Simplifying
x = 4.089988864


Subproblem 2
x + 0.4 = -4.489988864

Simplifying
x + 0.4 = -4.489988864

Reorder the terms:
0.4 + x = -4.489988864

Solving
0.4 + x = -4.489988864

Solving for variable 'x'.

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

Add '-0.4' to each side of the equation.
0.4 + -0.4 + x = -4.489988864 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + x = -4.489988864 + -0.4
x = -4.489988864 + -0.4

Combine like terms: -4.489988864 + -0.4 = -4.889988864
x = -4.889988864

Simplifying
x = -4.889988864


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.089988864, -4.889988864}
Solution
x = {4.089988864, -4.889988864}

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