5x(4x+10)=190

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Solution for 5x(4x+10)=190 equation: 


Simplifying
5x(4x + 10) = 190

Reorder the terms:
5x(10 + 4x) = 190
(10 * 5x + 4x * 5x) = 190
(50x + 20x2) = 190

Solving
50x + 20x2 = 190

Solving for variable 'x'.

Reorder the terms:
-190 + 50x + 20x2 = 190 + -190

Combine like terms: 190 + -190 = 0
-190 + 50x + 20x2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(-19 + 5x + 2x2) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(-19 + 5x + 2x2)' equal to zero and attempt to solve:

Simplifying
-19 + 5x + 2x2 = 0

Solving
-19 + 5x + 2x2 = 0

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

Divide each side by '2'.
-9.5 + 2.5x + x2 = 0

Move the constant term to the right:

Add '9.5' to each side of the equation.
-9.5 + 2.5x + 9.5 + x2 = 0 + 9.5

Reorder the terms:
-9.5 + 9.5 + 2.5x + x2 = 0 + 9.5

Combine like terms: -9.5 + 9.5 = 0.0
0.0 + 2.5x + x2 = 0 + 9.5
2.5x + x2 = 0 + 9.5

Combine like terms: 0 + 9.5 = 9.5
2.5x + x2 = 9.5

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = 9.5 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 9.5 + 1.5625

Combine like terms: 9.5 + 1.5625 = 11.0625
1.5625 + 2.5x + x2 = 11.0625

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 11.0625

Calculate the square root of the right side: 3.326033674

Break this problem into two subproblems by setting 
(x + 1.25) equal to 3.326033674 and -3.326033674.


Subproblem 1
x + 1.25 = 3.326033674

Simplifying
x + 1.25 = 3.326033674

Reorder the terms:
1.25 + x = 3.326033674

Solving
1.25 + x = 3.326033674

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = 3.326033674 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = 3.326033674 + -1.25
x = 3.326033674 + -1.25

Combine like terms: 3.326033674 + -1.25 = 2.076033674
x = 2.076033674

Simplifying
x = 2.076033674


Subproblem 2
x + 1.25 = -3.326033674

Simplifying
x + 1.25 = -3.326033674

Reorder the terms:
1.25 + x = -3.326033674

Solving
1.25 + x = -3.326033674

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = -3.326033674 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = -3.326033674 + -1.25
x = -3.326033674 + -1.25

Combine like terms: -3.326033674 + -1.25 = -4.576033674
x = -4.576033674

Simplifying
x = -4.576033674


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.076033674, -4.576033674}
Solution
x = {2.076033674, -4.576033674}

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