3x(x-7)=40

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Solution for 3x(x-7)=40 equation: 


Simplifying
3x(x + -7) = 40

Reorder the terms:
3x(-7 + x) = 40
(-7 * 3x + x * 3x) = 40
(-21x + 3x2) = 40

Solving
-21x + 3x2 = 40

Solving for variable 'x'.

Reorder the terms:
-40 + -21x + 3x2 = 40 + -40

Combine like terms: 40 + -40 = 0
-40 + -21x + 3x2 = 0

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

Divide each side by '3'.
-13.33333333 + -7x + x2 = 0

Move the constant term to the right:

Add '13.33333333' to each side of the equation.
-13.33333333 + -7x + 13.33333333 + x2 = 0 + 13.33333333

Reorder the terms:
-13.33333333 + 13.33333333 + -7x + x2 = 0 + 13.33333333

Combine like terms: -13.33333333 + 13.33333333 = 0.00000000
0.00000000 + -7x + x2 = 0 + 13.33333333
-7x + x2 = 0 + 13.33333333

Combine like terms: 0 + 13.33333333 = 13.33333333
-7x + x2 = 13.33333333

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = 13.33333333 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 13.33333333 + 12.25

Combine like terms: 13.33333333 + 12.25 = 25.58333333
12.25 + -7x + x2 = 25.58333333

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 25.58333333

Calculate the square root of the right side: 5.057996968

Break this problem into two subproblems by setting 
(x + -3.5) equal to 5.057996968 and -5.057996968.


Subproblem 1
x + -3.5 = 5.057996968

Simplifying
x + -3.5 = 5.057996968

Reorder the terms:
-3.5 + x = 5.057996968

Solving
-3.5 + x = 5.057996968

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = 5.057996968 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 5.057996968 + 3.5
x = 5.057996968 + 3.5

Combine like terms: 5.057996968 + 3.5 = 8.557996968
x = 8.557996968

Simplifying
x = 8.557996968


Subproblem 2
x + -3.5 = -5.057996968

Simplifying
x + -3.5 = -5.057996968

Reorder the terms:
-3.5 + x = -5.057996968

Solving
-3.5 + x = -5.057996968

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = -5.057996968 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -5.057996968 + 3.5
x = -5.057996968 + 3.5

Combine like terms: -5.057996968 + 3.5 = -1.557996968
x = -1.557996968

Simplifying
x = -1.557996968


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.557996968, -1.557996968}

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