2x(5x+6)=400

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Solution for 2x(5x+6)=400 equation: 


Simplifying
2x(5x + 6) = 400

Reorder the terms:
2x(6 + 5x) = 400
(6 * 2x + 5x * 2x) = 400
(12x + 10x2) = 400

Solving
12x + 10x2 = 400

Solving for variable 'x'.

Reorder the terms:
-400 + 12x + 10x2 = 400 + -400

Combine like terms: 400 + -400 = 0
-400 + 12x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-200 + 6x + 5x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-200 + 6x + 5x2)' equal to zero and attempt to solve:

Simplifying
-200 + 6x + 5x2 = 0

Solving
-200 + 6x + 5x2 = 0

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

Divide each side by '5'.
-40 + 1.2x + x2 = 0

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + 1.2x + 40 + x2 = 0 + 40

Reorder the terms:
-40 + 40 + 1.2x + x2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + 1.2x + x2 = 0 + 40
1.2x + x2 = 0 + 40

Combine like terms: 0 + 40 = 40
1.2x + x2 = 40

The x term is 1.2x.  Take half its coefficient (0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
1.2x + 0.36 + x2 = 40 + 0.36

Reorder the terms:
0.36 + 1.2x + x2 = 40 + 0.36

Combine like terms: 40 + 0.36 = 40.36
0.36 + 1.2x + x2 = 40.36

Factor a perfect square on the left side:
(x + 0.6)(x + 0.6) = 40.36

Calculate the square root of the right side: 6.35295207

Break this problem into two subproblems by setting 
(x + 0.6) equal to 6.35295207 and -6.35295207.


Subproblem 1
x + 0.6 = 6.35295207

Simplifying
x + 0.6 = 6.35295207

Reorder the terms:
0.6 + x = 6.35295207

Solving
0.6 + x = 6.35295207

Solving for variable 'x'.

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

Add '-0.6' to each side of the equation.
0.6 + -0.6 + x = 6.35295207 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + x = 6.35295207 + -0.6
x = 6.35295207 + -0.6

Combine like terms: 6.35295207 + -0.6 = 5.75295207
x = 5.75295207

Simplifying
x = 5.75295207


Subproblem 2
x + 0.6 = -6.35295207

Simplifying
x + 0.6 = -6.35295207

Reorder the terms:
0.6 + x = -6.35295207

Solving
0.6 + x = -6.35295207

Solving for variable 'x'.

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

Add '-0.6' to each side of the equation.
0.6 + -0.6 + x = -6.35295207 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + x = -6.35295207 + -0.6
x = -6.35295207 + -0.6

Combine like terms: -6.35295207 + -0.6 = -6.95295207
x = -6.95295207

Simplifying
x = -6.95295207


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.75295207, -6.95295207}
Solution
x = {5.75295207, -6.95295207}

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