=(5x^2+2)(4)+(4x-5)(10x)

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Solution for =(5x^2+2)(4)+(4x-5)(10x) equation:


Simplifying
0 = (5x2 + 2)(4) + (4x + -5)(10x)

Reorder the terms:
0 = (2 + 5x2)(4) + (4x + -5)(10x)

Reorder the terms for easier multiplication:
0 = 4(2 + 5x2) + (4x + -5)(10x)
0 = (2 * 4 + 5x2 * 4) + (4x + -5)(10x)
0 = (8 + 20x2) + (4x + -5)(10x)

Reorder the terms:
0 = 8 + 20x2 + (-5 + 4x)(10x)

Remove parenthesis around (10x)
0 = 8 + 20x2 + (-5 + 4x) * 10x

Reorder the terms for easier multiplication:
0 = 8 + 20x2 + 10x(-5 + 4x)
0 = 8 + 20x2 + (-5 * 10x + 4x * 10x)
0 = 8 + 20x2 + (-50x + 40x2)

Reorder the terms:
0 = 8 + -50x + 20x2 + 40x2

Combine like terms: 20x2 + 40x2 = 60x2
0 = 8 + -50x + 60x2

Solving
0 = 8 + -50x + 60x2

Solving for variable 'x'.

Combine like terms: 0 + -8 = -8
-8 + 50x + -60x2 = 8 + -50x + 60x2 + -8 + 50x + -60x2

Reorder the terms:
-8 + 50x + -60x2 = 8 + -8 + -50x + 50x + 60x2 + -60x2

Combine like terms: 8 + -8 = 0
-8 + 50x + -60x2 = 0 + -50x + 50x + 60x2 + -60x2
-8 + 50x + -60x2 = -50x + 50x + 60x2 + -60x2

Combine like terms: -50x + 50x = 0
-8 + 50x + -60x2 = 0 + 60x2 + -60x2
-8 + 50x + -60x2 = 60x2 + -60x2

Combine like terms: 60x2 + -60x2 = 0
-8 + 50x + -60x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + 25x + -30x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-4 + 25x + -30x2)' equal to zero and attempt to solve:

Simplifying
-4 + 25x + -30x2 = 0

Solving
-4 + 25x + -30x2 = 0

Begin completing the square.  Divide all terms by
-30 the coefficient of the squared term: 

Divide each side by '-30'.
0.1333333333 + -0.8333333333x + x2 = 0.0

Move the constant term to the right:

Add '-0.1333333333' to each side of the equation.
0.1333333333 + -0.8333333333x + -0.1333333333 + x2 = 0.0 + -0.1333333333

Reorder the terms:
0.1333333333 + -0.1333333333 + -0.8333333333x + x2 = 0.0 + -0.1333333333

Combine like terms: 0.1333333333 + -0.1333333333 = 0.0000000000
0.0000000000 + -0.8333333333x + x2 = 0.0 + -0.1333333333
-0.8333333333x + x2 = 0.0 + -0.1333333333

Combine like terms: 0.0 + -0.1333333333 = -0.1333333333
-0.8333333333x + x2 = -0.1333333333

The x term is -0.8333333333x.  Take half its coefficient (-0.4166666667).
Square it (0.1736111111) and add it to both sides.

Add '0.1736111111' to each side of the equation.
-0.8333333333x + 0.1736111111 + x2 = -0.1333333333 + 0.1736111111

Reorder the terms:
0.1736111111 + -0.8333333333x + x2 = -0.1333333333 + 0.1736111111

Combine like terms: -0.1333333333 + 0.1736111111 = 0.0402777778
0.1736111111 + -0.8333333333x + x2 = 0.0402777778

Factor a perfect square on the left side:
(x + -0.4166666667)(x + -0.4166666667) = 0.0402777778

Calculate the square root of the right side: 0.200693243

Break this problem into two subproblems by setting 
(x + -0.4166666667) equal to 0.200693243 and -0.200693243.


Subproblem 1
x + -0.4166666667 = 0.200693243

Simplifying
x + -0.4166666667 = 0.200693243

Reorder the terms:
-0.4166666667 + x = 0.200693243

Solving
-0.4166666667 + x = 0.200693243

Solving for variable 'x'.

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

Add '0.4166666667' to each side of the equation.
-0.4166666667 + 0.4166666667 + x = 0.200693243 + 0.4166666667

Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000
0.0000000000 + x = 0.200693243 + 0.4166666667
x = 0.200693243 + 0.4166666667

Combine like terms: 0.200693243 + 0.4166666667 = 0.6173599097
x = 0.6173599097

Simplifying
x = 0.6173599097


Subproblem 2
x + -0.4166666667 = -0.200693243

Simplifying
x + -0.4166666667 = -0.200693243

Reorder the terms:
-0.4166666667 + x = -0.200693243

Solving
-0.4166666667 + x = -0.200693243

Solving for variable 'x'.

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

Add '0.4166666667' to each side of the equation.
-0.4166666667 + 0.4166666667 + x = -0.200693243 + 0.4166666667

Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000
0.0000000000 + x = -0.200693243 + 0.4166666667
x = -0.200693243 + 0.4166666667

Combine like terms: -0.200693243 + 0.4166666667 = 0.2159734237
x = 0.2159734237

Simplifying
x = 0.2159734237


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.6173599097, 0.2159734237}
Solution
x = {0.6173599097, 0.2159734237}

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