(2x-1)(x+1)=45

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Solution for (2x-1)(x+1)=45 equation:


Simplifying
(2x + -1)(x + 1) = 45

Reorder the terms:
(-1 + 2x)(x + 1) = 45

Reorder the terms:
(-1 + 2x)(1 + x) = 45

Multiply (-1 + 2x) * (1 + x)
(-1(1 + x) + 2x * (1 + x)) = 45
((1 * -1 + x * -1) + 2x * (1 + x)) = 45
((-1 + -1x) + 2x * (1 + x)) = 45
(-1 + -1x + (1 * 2x + x * 2x)) = 45
(-1 + -1x + (2x + 2x2)) = 45

Combine like terms: -1x + 2x = 1x
(-1 + 1x + 2x2) = 45

Solving
-1 + 1x + 2x2 = 45

Solving for variable 'x'.

Reorder the terms:
-1 + -45 + 1x + 2x2 = 45 + -45

Combine like terms: -1 + -45 = -46
-46 + 1x + 2x2 = 45 + -45

Combine like terms: 45 + -45 = 0
-46 + 1x + 2x2 = 0

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

Divide each side by '2'.
-23 + 0.5x + x2 = 0

Move the constant term to the right:

Add '23' to each side of the equation.
-23 + 0.5x + 23 + x2 = 0 + 23

Reorder the terms:
-23 + 23 + 0.5x + x2 = 0 + 23

Combine like terms: -23 + 23 = 0
0 + 0.5x + x2 = 0 + 23
0.5x + x2 = 0 + 23

Combine like terms: 0 + 23 = 23
0.5x + x2 = 23

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 23 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 23 + 0.0625

Combine like terms: 23 + 0.0625 = 23.0625
0.0625 + 0.5x + x2 = 23.0625

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 23.0625

Calculate the square root of the right side: 4.802343178

Break this problem into two subproblems by setting 
(x + 0.25) equal to 4.802343178 and -4.802343178.

Subproblem 1

x + 0.25 = 4.802343178 Simplifying x + 0.25 = 4.802343178 Reorder the terms: 0.25 + x = 4.802343178 Solving 0.25 + x = 4.802343178 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 4.802343178 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 4.802343178 + -0.25 x = 4.802343178 + -0.25 Combine like terms: 4.802343178 + -0.25 = 4.552343178 x = 4.552343178 Simplifying x = 4.552343178

Subproblem 2

x + 0.25 = -4.802343178 Simplifying x + 0.25 = -4.802343178 Reorder the terms: 0.25 + x = -4.802343178 Solving 0.25 + x = -4.802343178 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -4.802343178 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -4.802343178 + -0.25 x = -4.802343178 + -0.25 Combine like terms: -4.802343178 + -0.25 = -5.052343178 x = -5.052343178 Simplifying x = -5.052343178

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.552343178, -5.052343178}

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