(2x+1)(4-x)=10-(2x*2x)

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Solution for (2x+1)(4-x)=10-(2x*2x) equation:


Simplifying
(2x + 1)(4 + -1x) = 10 + -1(2x * 2x)

Reorder the terms:
(1 + 2x)(4 + -1x) = 10 + -1(2x * 2x)

Multiply (1 + 2x) * (4 + -1x)
(1(4 + -1x) + 2x * (4 + -1x)) = 10 + -1(2x * 2x)
((4 * 1 + -1x * 1) + 2x * (4 + -1x)) = 10 + -1(2x * 2x)
((4 + -1x) + 2x * (4 + -1x)) = 10 + -1(2x * 2x)
(4 + -1x + (4 * 2x + -1x * 2x)) = 10 + -1(2x * 2x)
(4 + -1x + (8x + -2x2)) = 10 + -1(2x * 2x)

Combine like terms: -1x + 8x = 7x
(4 + 7x + -2x2) = 10 + -1(2x * 2x)

Reorder the terms for easier multiplication:
4 + 7x + -2x2 = 10 + -1(2 * 2x * x)

Multiply 2 * 2
4 + 7x + -2x2 = 10 + -1(4x * x)

Multiply x * x
4 + 7x + -2x2 = 10 + -1(4x2)

Remove parenthesis around (4x2)
4 + 7x + -2x2 = 10 + -1 * 4x2

Multiply -1 * 4
4 + 7x + -2x2 = 10 + -4x2

Solving
4 + 7x + -2x2 = 10 + -4x2

Solving for variable 'x'.

Reorder the terms:
4 + -10 + 7x + -2x2 + 4x2 = 10 + -4x2 + -10 + 4x2

Combine like terms: 4 + -10 = -6
-6 + 7x + -2x2 + 4x2 = 10 + -4x2 + -10 + 4x2

Combine like terms: -2x2 + 4x2 = 2x2
-6 + 7x + 2x2 = 10 + -4x2 + -10 + 4x2

Reorder the terms:
-6 + 7x + 2x2 = 10 + -10 + -4x2 + 4x2

Combine like terms: 10 + -10 = 0
-6 + 7x + 2x2 = 0 + -4x2 + 4x2
-6 + 7x + 2x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
-6 + 7x + 2x2 = 0

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

Divide each side by '2'.
-3 + 3.5x + x2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 3.5x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + 3.5x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 3.5x + x2 = 0 + 3
3.5x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
3.5x + x2 = 3

The x term is 3.5x.  Take half its coefficient (1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
3.5x + 3.0625 + x2 = 3 + 3.0625

Reorder the terms:
3.0625 + 3.5x + x2 = 3 + 3.0625

Combine like terms: 3 + 3.0625 = 6.0625
3.0625 + 3.5x + x2 = 6.0625

Factor a perfect square on the left side:
(x + 1.75)(x + 1.75) = 6.0625

Calculate the square root of the right side: 2.46221445

Break this problem into two subproblems by setting 
(x + 1.75) equal to 2.46221445 and -2.46221445.

Subproblem 1

x + 1.75 = 2.46221445 Simplifying x + 1.75 = 2.46221445 Reorder the terms: 1.75 + x = 2.46221445 Solving 1.75 + x = 2.46221445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 2.46221445 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 2.46221445 + -1.75 x = 2.46221445 + -1.75 Combine like terms: 2.46221445 + -1.75 = 0.71221445 x = 0.71221445 Simplifying x = 0.71221445

Subproblem 2

x + 1.75 = -2.46221445 Simplifying x + 1.75 = -2.46221445 Reorder the terms: 1.75 + x = -2.46221445 Solving 1.75 + x = -2.46221445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -2.46221445 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -2.46221445 + -1.75 x = -2.46221445 + -1.75 Combine like terms: -2.46221445 + -1.75 = -4.21221445 x = -4.21221445 Simplifying x = -4.21221445

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.71221445, -4.21221445}

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