3x(x-5)=7

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Solution for 3x(x-5)=7 equation: 


Simplifying
3x(x + -5) = 7

Reorder the terms:
3x(-5 + x) = 7
(-5 * 3x + x * 3x) = 7
(-15x + 3x2) = 7

Solving
-15x + 3x2 = 7

Solving for variable 'x'.

Reorder the terms:
-7 + -15x + 3x2 = 7 + -7

Combine like terms: 7 + -7 = 0
-7 + -15x + 3x2 = 0

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

Divide each side by '3'.
-2.333333333 + -5x + x2 = 0

Move the constant term to the right:

Add '2.333333333' to each side of the equation.
-2.333333333 + -5x + 2.333333333 + x2 = 0 + 2.333333333

Reorder the terms:
-2.333333333 + 2.333333333 + -5x + x2 = 0 + 2.333333333

Combine like terms: -2.333333333 + 2.333333333 = 0.000000000
0.000000000 + -5x + x2 = 0 + 2.333333333
-5x + x2 = 0 + 2.333333333

Combine like terms: 0 + 2.333333333 = 2.333333333
-5x + x2 = 2.333333333

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 2.333333333 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 2.333333333 + 6.25

Combine like terms: 2.333333333 + 6.25 = 8.583333333
6.25 + -5x + x2 = 8.583333333

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 8.583333333

Calculate the square root of the right side: 2.929732638

Break this problem into two subproblems by setting 
(x + -2.5) equal to 2.929732638 and -2.929732638.


Subproblem 1
x + -2.5 = 2.929732638

Simplifying
x + -2.5 = 2.929732638

Reorder the terms:
-2.5 + x = 2.929732638

Solving
-2.5 + x = 2.929732638

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 2.929732638 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 2.929732638 + 2.5
x = 2.929732638 + 2.5

Combine like terms: 2.929732638 + 2.5 = 5.429732638
x = 5.429732638

Simplifying
x = 5.429732638


Subproblem 2
x + -2.5 = -2.929732638

Simplifying
x + -2.5 = -2.929732638

Reorder the terms:
-2.5 + x = -2.929732638

Solving
-2.5 + x = -2.929732638

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -2.929732638 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -2.929732638 + 2.5
x = -2.929732638 + 2.5

Combine like terms: -2.929732638 + 2.5 = -0.429732638
x = -0.429732638

Simplifying
x = -0.429732638


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.429732638, -0.429732638}

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