-5x(-2x+7)=55

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Solution for -5x(-2x+7)=55 equation: 


Simplifying
-5x(-2x + 7) = 55

Reorder the terms:
-5x(7 + -2x) = 55
(7 * -5x + -2x * -5x) = 55
(-35x + 10x2) = 55

Solving
-35x + 10x2 = 55

Solving for variable 'x'.

Reorder the terms:
-55 + -35x + 10x2 = 55 + -55

Combine like terms: 55 + -55 = 0
-55 + -35x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-11 + -7x + 2x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-11 + -7x + 2x2)' equal to zero and attempt to solve:

Simplifying
-11 + -7x + 2x2 = 0

Solving
-11 + -7x + 2x2 = 0

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

Divide each side by '2'.
-5.5 + -3.5x + x2 = 0

Move the constant term to the right:

Add '5.5' to each side of the equation.
-5.5 + -3.5x + 5.5 + x2 = 0 + 5.5

Reorder the terms:
-5.5 + 5.5 + -3.5x + x2 = 0 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + -3.5x + x2 = 0 + 5.5
-3.5x + x2 = 0 + 5.5

Combine like terms: 0 + 5.5 = 5.5
-3.5x + x2 = 5.5

The x term is -3.5x.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5x + 3.0625 + x2 = 5.5 + 3.0625

Reorder the terms:
3.0625 + -3.5x + x2 = 5.5 + 3.0625

Combine like terms: 5.5 + 3.0625 = 8.5625
3.0625 + -3.5x + x2 = 8.5625

Factor a perfect square on the left side:
(x + -1.75)(x + -1.75) = 8.5625

Calculate the square root of the right side: 2.926174978

Break this problem into two subproblems by setting 
(x + -1.75) equal to 2.926174978 and -2.926174978.


Subproblem 1
x + -1.75 = 2.926174978

Simplifying
x + -1.75 = 2.926174978

Reorder the terms:
-1.75 + x = 2.926174978

Solving
-1.75 + x = 2.926174978

Solving for variable 'x'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + x = 2.926174978 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + x = 2.926174978 + 1.75
x = 2.926174978 + 1.75

Combine like terms: 2.926174978 + 1.75 = 4.676174978
x = 4.676174978

Simplifying
x = 4.676174978


Subproblem 2
x + -1.75 = -2.926174978

Simplifying
x + -1.75 = -2.926174978

Reorder the terms:
-1.75 + x = -2.926174978

Solving
-1.75 + x = -2.926174978

Solving for variable 'x'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + x = -2.926174978 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + x = -2.926174978 + 1.75
x = -2.926174978 + 1.75

Combine like terms: -2.926174978 + 1.75 = -1.176174978
x = -1.176174978

Simplifying
x = -1.176174978


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.676174978, -1.176174978}
Solution
x = {4.676174978, -1.176174978}

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