7x+(x-4)(x+5)-5x=

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Solution for 7x+(x-4)(x+5)-5x= equation: 


Simplifying
7x + (x + -4)(x + 5) + -5x = 0

Reorder the terms:
7x + (-4 + x)(x + 5) + -5x = 0

Reorder the terms:
7x + (-4 + x)(5 + x) + -5x = 0

Multiply (-4 + x) * (5 + x)
7x + (-4(5 + x) + x(5 + x)) + -5x = 0
7x + ((5 * -4 + x * -4) + x(5 + x)) + -5x = 0
7x + ((-20 + -4x) + x(5 + x)) + -5x = 0
7x + (-20 + -4x + (5 * x + x * x)) + -5x = 0
7x + (-20 + -4x + (5x + x2)) + -5x = 0

Combine like terms: -4x + 5x = 1x
7x + (-20 + 1x + x2) + -5x = 0

Reorder the terms:
-20 + 7x + 1x + -5x + x2 = 0

Combine like terms: 7x + 1x = 8x
-20 + 8x + -5x + x2 = 0

Combine like terms: 8x + -5x = 3x
-20 + 3x + x2 = 0

Solving
-20 + 3x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + 3x + 20 + x2 = 0 + 20

Reorder the terms:
-20 + 20 + 3x + x2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + 3x + x2 = 0 + 20
3x + x2 = 0 + 20

Combine like terms: 0 + 20 = 20
3x + x2 = 20

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 20 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 20 + 2.25

Combine like terms: 20 + 2.25 = 22.25
2.25 + 3x + x2 = 22.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 22.25

Calculate the square root of the right side: 4.716990566

Break this problem into two subproblems by setting 
(x + 1.5) equal to 4.716990566 and -4.716990566.


Subproblem 1
x + 1.5 = 4.716990566

Simplifying
x + 1.5 = 4.716990566

Reorder the terms:
1.5 + x = 4.716990566

Solving
1.5 + x = 4.716990566

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 4.716990566 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 4.716990566 + -1.5
x = 4.716990566 + -1.5

Combine like terms: 4.716990566 + -1.5 = 3.216990566
x = 3.216990566

Simplifying
x = 3.216990566


Subproblem 2
x + 1.5 = -4.716990566

Simplifying
x + 1.5 = -4.716990566

Reorder the terms:
1.5 + x = -4.716990566

Solving
1.5 + x = -4.716990566

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -4.716990566 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -4.716990566 + -1.5
x = -4.716990566 + -1.5

Combine like terms: -4.716990566 + -1.5 = -6.216990566
x = -6.216990566

Simplifying
x = -6.216990566


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.216990566, -6.216990566}

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