140x+1200=(2x*2x)

Solution for 140x+1200=(2x*2x) equation:

Simplifying
140x + 1200 = (2x * 2x)

Reorder the terms:
1200 + 140x = (2x * 2x)

Reorder the terms for easier multiplication:
1200 + 140x = (2 * 2x * x)

Multiply 2 * 2
1200 + 140x = (4x * x)

Multiply x * x
1200 + 140x = (4x2)

Solving
1200 + 140x = (4x2)

Solving for variable 'x'.

Combine like terms: (4x2) + (-4x2) = 0
1200 + 140x + (-4x2) = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(300 + 35x + (-1x2)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(300 + 35x + (-1x2))' equal to zero and attempt to solve:

Simplifying
300 + 35x + (-1x2) = 0

Solving
300 + 35x + (-1x2) = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-300 + -35x + x2 = 0

Move the constant term to the right:

Add '300' to each side of the equation.
-300 + -35x + 300 + x2 = 0 + 300

Reorder the terms:
-300 + 300 + -35x + x2 = 0 + 300

Combine like terms: -300 + 300 = 0
0 + -35x + x2 = 0 + 300
-35x + x2 = 0 + 300

Combine like terms: 0 + 300 = 300
-35x + x2 = 300

The x term is -35x.  Take half its coefficient (-17.5).
Square it (306.25) and add it to both sides.

Add '306.25' to each side of the equation.
-35x + 306.25 + x2 = 300 + 306.25

Reorder the terms:
306.25 + -35x + x2 = 300 + 306.25

Combine like terms: 300 + 306.25 = 606.25
306.25 + -35x + x2 = 606.25

Factor a perfect square on the left side:
((x) + -17.5)((x) + -17.5) = 606.25

Calculate the square root of the right side: 24.622144504

Break this problem into two subproblems by setting 
((x) + -17.5) equal to 24.622144504 and -24.622144504.

Subproblem 1
(x) + -17.5 = 24.622144504

Simplifying
(x) + -17.5 = 24.622144504
x + -17.5 = 24.622144504

Reorder the terms:
-17.5 + x = 24.622144504

Solving
-17.5 + x = 24.622144504

Solving for variable 'x'.

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

Add '17.5' to each side of the equation.
-17.5 + 17.5 + x = 24.622144504 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + x = 24.622144504 + 17.5
x = 24.622144504 + 17.5

Combine like terms: 24.622144504 + 17.5 = 42.122144504
x = 42.122144504

Simplifying
x = 42.122144504

Subproblem 2
(x) + -17.5 = -24.622144504

Simplifying
(x) + -17.5 = -24.622144504
x + -17.5 = -24.622144504

Reorder the terms:
-17.5 + x = -24.622144504

Solving
-17.5 + x = -24.622144504

Solving for variable 'x'.

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

Add '17.5' to each side of the equation.
-17.5 + 17.5 + x = -24.622144504 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + x = -24.622144504 + 17.5
x = -24.622144504 + 17.5

Combine like terms: -24.622144504 + 17.5 = -7.122144504
x = -7.122144504

Simplifying
x = -7.122144504

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {42.122144504, -7.122144504}
Solution
x = {42.122144504, -7.122144504}