(x)(x+1)=2x+29

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Solution for (x)(x+1)=2x+29 equation:


Simplifying
(x)(x + 1) = 2x + 29

Reorder the terms:
x(1 + x) = 2x + 29
(1 * x + x * x) = 2x + 29
(1x + x2) = 2x + 29

Reorder the terms:
1x + x2 = 29 + 2x

Solving
1x + x2 = 29 + 2x

Solving for variable 'x'.

Reorder the terms:
-29 + 1x + -2x + x2 = 29 + 2x + -29 + -2x

Combine like terms: 1x + -2x = -1x
-29 + -1x + x2 = 29 + 2x + -29 + -2x

Reorder the terms:
-29 + -1x + x2 = 29 + -29 + 2x + -2x

Combine like terms: 29 + -29 = 0
-29 + -1x + x2 = 0 + 2x + -2x
-29 + -1x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-29 + -1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '29' to each side of the equation.
-29 + -1x + 29 + x2 = 0 + 29

Reorder the terms:
-29 + 29 + -1x + x2 = 0 + 29

Combine like terms: -29 + 29 = 0
0 + -1x + x2 = 0 + 29
-1x + x2 = 0 + 29

Combine like terms: 0 + 29 = 29
-1x + x2 = 29

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 29 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 29 + 0.25

Combine like terms: 29 + 0.25 = 29.25
0.25 + -1x + x2 = 29.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 29.25

Calculate the square root of the right side: 5.408326913

Break this problem into two subproblems by setting 
(x + -0.5) equal to 5.408326913 and -5.408326913.

Subproblem 1

x + -0.5 = 5.408326913 Simplifying x + -0.5 = 5.408326913 Reorder the terms: -0.5 + x = 5.408326913 Solving -0.5 + x = 5.408326913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 5.408326913 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 5.408326913 + 0.5 x = 5.408326913 + 0.5 Combine like terms: 5.408326913 + 0.5 = 5.908326913 x = 5.908326913 Simplifying x = 5.908326913

Subproblem 2

x + -0.5 = -5.408326913 Simplifying x + -0.5 = -5.408326913 Reorder the terms: -0.5 + x = -5.408326913 Solving -0.5 + x = -5.408326913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -5.408326913 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -5.408326913 + 0.5 x = -5.408326913 + 0.5 Combine like terms: -5.408326913 + 0.5 = -4.908326913 x = -4.908326913 Simplifying x = -4.908326913

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.908326913, -4.908326913}

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