4x^2=49.7(2-x)(1-x)

Solution for 4x^2=49.7(2-x)(1-x) equation:

Simplifying
4x2 = 49.7(2 + -1x)(1 + -1x)

Multiply (2 + -1x) * (1 + -1x)
4x2 = 49.7(2(1 + -1x) + -1x * (1 + -1x))
4x2 = 49.7((1 * 2 + -1x * 2) + -1x * (1 + -1x))
4x2 = 49.7((2 + -2x) + -1x * (1 + -1x))
4x2 = 49.7(2 + -2x + (1 * -1x + -1x * -1x))
4x2 = 49.7(2 + -2x + (-1x + 1x2))

Combine like terms: -2x + -1x = -3x
4x2 = 49.7(2 + -3x + 1x2)
4x2 = (2 * 49.7 + -3x * 49.7 + 1x2 * 49.7)
4x2 = (99.4 + -149.1x + 49.7x2)

Solving
4x2 = 99.4 + -149.1x + 49.7x2

Solving for variable 'x'.

Reorder the terms:
-99.4 + 149.1x + 4x2 + -49.7x2 = 99.4 + -149.1x + 49.7x2 + -99.4 + 149.1x + -49.7x2

Combine like terms: 4x2 + -49.7x2 = -45.7x2
-99.4 + 149.1x + -45.7x2 = 99.4 + -149.1x + 49.7x2 + -99.4 + 149.1x + -49.7x2

Reorder the terms:
-99.4 + 149.1x + -45.7x2 = 99.4 + -99.4 + -149.1x + 149.1x + 49.7x2 + -49.7x2

Combine like terms: 99.4 + -99.4 = 0.0
-99.4 + 149.1x + -45.7x2 = 0.0 + -149.1x + 149.1x + 49.7x2 + -49.7x2
-99.4 + 149.1x + -45.7x2 = -149.1x + 149.1x + 49.7x2 + -49.7x2

Combine like terms: -149.1x + 149.1x = 0.0
-99.4 + 149.1x + -45.7x2 = 0.0 + 49.7x2 + -49.7x2
-99.4 + 149.1x + -45.7x2 = 49.7x2 + -49.7x2

Combine like terms: 49.7x2 + -49.7x2 = 0.0
-99.4 + 149.1x + -45.7x2 = 0.0

Begin completing the square.  Divide all terms by
-45.7 the coefficient of the squared term: 

Divide each side by '-45.7'.
2.175054705 + -3.262582057x + x2 = 0

Move the constant term to the right:

Add '-2.175054705' to each side of the equation.
2.175054705 + -3.262582057x + -2.175054705 + x2 = 0 + -2.175054705

Reorder the terms:
2.175054705 + -2.175054705 + -3.262582057x + x2 = 0 + -2.175054705

Combine like terms: 2.175054705 + -2.175054705 = 0.000000000
0.000000000 + -3.262582057x + x2 = 0 + -2.175054705
-3.262582057x + x2 = 0 + -2.175054705

Combine like terms: 0 + -2.175054705 = -2.175054705
-3.262582057x + x2 = -2.175054705

The x term is -3.262582057x.  Take half its coefficient (-1.631291029).
Square it (2.661110421) and add it to both sides.

Add '2.661110421' to each side of the equation.
-3.262582057x + 2.661110421 + x2 = -2.175054705 + 2.661110421

Reorder the terms:
2.661110421 + -3.262582057x + x2 = -2.175054705 + 2.661110421

Combine like terms: -2.175054705 + 2.661110421 = 0.486055716
2.661110421 + -3.262582057x + x2 = 0.486055716

Factor a perfect square on the left side:
(x + -1.631291029)(x + -1.631291029) = 0.486055716

Calculate the square root of the right side: 0.697176962

Break this problem into two subproblems by setting 
(x + -1.631291029) equal to 0.697176962 and -0.697176962.

Subproblem 1
x + -1.631291029 = 0.697176962

Simplifying
x + -1.631291029 = 0.697176962

Reorder the terms:
-1.631291029 + x = 0.697176962

Solving
-1.631291029 + x = 0.697176962

Solving for variable 'x'.

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

Add '1.631291029' to each side of the equation.
-1.631291029 + 1.631291029 + x = 0.697176962 + 1.631291029

Combine like terms: -1.631291029 + 1.631291029 = 0.000000000
0.000000000 + x = 0.697176962 + 1.631291029
x = 0.697176962 + 1.631291029

Combine like terms: 0.697176962 + 1.631291029 = 2.328467991
x = 2.328467991

Simplifying
x = 2.328467991

Subproblem 2
x + -1.631291029 = -0.697176962

Simplifying
x + -1.631291029 = -0.697176962

Reorder the terms:
-1.631291029 + x = -0.697176962

Solving
-1.631291029 + x = -0.697176962

Solving for variable 'x'.

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

Add '1.631291029' to each side of the equation.
-1.631291029 + 1.631291029 + x = -0.697176962 + 1.631291029

Combine like terms: -1.631291029 + 1.631291029 = 0.000000000
0.000000000 + x = -0.697176962 + 1.631291029
x = -0.697176962 + 1.631291029

Combine like terms: -0.697176962 + 1.631291029 = 0.934114067
x = 0.934114067

Simplifying
x = 0.934114067

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.328467991, 0.934114067}