5(10x-10)=-5x(-4x+14)

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Solution for 5(10x-10)=-5x(-4x+14) equation:


Simplifying
5(10x + -10) = -5x(-4x + 14)

Reorder the terms:
5(-10 + 10x) = -5x(-4x + 14)
(-10 * 5 + 10x * 5) = -5x(-4x + 14)
(-50 + 50x) = -5x(-4x + 14)

Reorder the terms:
-50 + 50x = -5x(14 + -4x)
-50 + 50x = (14 * -5x + -4x * -5x)
-50 + 50x = (-70x + 20x2)

Solving
-50 + 50x = -70x + 20x2

Solving for variable 'x'.

Combine like terms: 50x + 70x = 120x
-50 + 120x + -20x2 = -70x + 20x2 + 70x + -20x2

Reorder the terms:
-50 + 120x + -20x2 = -70x + 70x + 20x2 + -20x2

Combine like terms: -70x + 70x = 0
-50 + 120x + -20x2 = 0 + 20x2 + -20x2
-50 + 120x + -20x2 = 20x2 + -20x2

Combine like terms: 20x2 + -20x2 = 0
-50 + 120x + -20x2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(-5 + 12x + -2x2) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(-5 + 12x + -2x2)' equal to zero and attempt to solve:

Simplifying
-5 + 12x + -2x2 = 0

Solving
-5 + 12x + -2x2 = 0

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

Divide each side by '-2'.
2.5 + -6x + x2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + -6x + -2.5 + x2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + -6x + x2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + -6x + x2 = 0 + -2.5
-6x + x2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
-6x + x2 = -2.5

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = -2.5 + 9

Reorder the terms:
9 + -6x + x2 = -2.5 + 9

Combine like terms: -2.5 + 9 = 6.5
9 + -6x + x2 = 6.5

Factor a perfect square on the left side:
(x + -3)(x + -3) = 6.5

Calculate the square root of the right side: 2.549509757

Break this problem into two subproblems by setting 
(x + -3) equal to 2.549509757 and -2.549509757.


Subproblem 1
x + -3 = 2.549509757

Simplifying
x + -3 = 2.549509757

Reorder the terms:
-3 + x = 2.549509757

Solving
-3 + x = 2.549509757

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 2.549509757 + 3

Combine like terms: -3 + 3 = 0
0 + x = 2.549509757 + 3
x = 2.549509757 + 3

Combine like terms: 2.549509757 + 3 = 5.549509757
x = 5.549509757

Simplifying
x = 5.549509757


Subproblem 2
x + -3 = -2.549509757

Simplifying
x + -3 = -2.549509757

Reorder the terms:
-3 + x = -2.549509757

Solving
-3 + x = -2.549509757

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -2.549509757 + 3

Combine like terms: -3 + 3 = 0
0 + x = -2.549509757 + 3
x = -2.549509757 + 3

Combine like terms: -2.549509757 + 3 = 0.450490243
x = 0.450490243

Simplifying
x = 0.450490243


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.549509757, 0.450490243}
Solution
x = {5.549509757, 0.450490243}

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