5x(4x-5)=155

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Solution for 5x(4x-5)=155 equation: 


Simplifying
5x(4x + -5) = 155

Reorder the terms:
5x(-5 + 4x) = 155
(-5 * 5x + 4x * 5x) = 155
(-25x + 20x2) = 155

Solving
-25x + 20x2 = 155

Solving for variable 'x'.

Reorder the terms:
-155 + -25x + 20x2 = 155 + -155

Combine like terms: 155 + -155 = 0
-155 + -25x + 20x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-31 + -5x + 4x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-31 + -5x + 4x2)' equal to zero and attempt to solve:

Simplifying
-31 + -5x + 4x2 = 0

Solving
-31 + -5x + 4x2 = 0

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

Divide each side by '4'.
-7.75 + -1.25x + x2 = 0

Move the constant term to the right:

Add '7.75' to each side of the equation.
-7.75 + -1.25x + 7.75 + x2 = 0 + 7.75

Reorder the terms:
-7.75 + 7.75 + -1.25x + x2 = 0 + 7.75

Combine like terms: -7.75 + 7.75 = 0.00
0.00 + -1.25x + x2 = 0 + 7.75
-1.25x + x2 = 0 + 7.75

Combine like terms: 0 + 7.75 = 7.75
-1.25x + x2 = 7.75

The x term is -1.25x.  Take half its coefficient (-0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
-1.25x + 0.390625 + x2 = 7.75 + 0.390625

Reorder the terms:
0.390625 + -1.25x + x2 = 7.75 + 0.390625

Combine like terms: 7.75 + 0.390625 = 8.140625
0.390625 + -1.25x + x2 = 8.140625

Factor a perfect square on the left side:
(x + -0.625)(x + -0.625) = 8.140625

Calculate the square root of the right side: 2.853178053

Break this problem into two subproblems by setting 
(x + -0.625) equal to 2.853178053 and -2.853178053.


Subproblem 1
x + -0.625 = 2.853178053

Simplifying
x + -0.625 = 2.853178053

Reorder the terms:
-0.625 + x = 2.853178053

Solving
-0.625 + x = 2.853178053

Solving for variable 'x'.

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

Add '0.625' to each side of the equation.
-0.625 + 0.625 + x = 2.853178053 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + x = 2.853178053 + 0.625
x = 2.853178053 + 0.625

Combine like terms: 2.853178053 + 0.625 = 3.478178053
x = 3.478178053

Simplifying
x = 3.478178053


Subproblem 2
x + -0.625 = -2.853178053

Simplifying
x + -0.625 = -2.853178053

Reorder the terms:
-0.625 + x = -2.853178053

Solving
-0.625 + x = -2.853178053

Solving for variable 'x'.

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

Add '0.625' to each side of the equation.
-0.625 + 0.625 + x = -2.853178053 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + x = -2.853178053 + 0.625
x = -2.853178053 + 0.625

Combine like terms: -2.853178053 + 0.625 = -2.228178053
x = -2.228178053

Simplifying
x = -2.228178053


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.478178053, -2.228178053}
Solution
x = {3.478178053, -2.228178053}

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