x(x+1)=2(x+5)

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Solution for x(x+1)=2(x+5) equation:


Simplifying
x(x + 1) = 2(x + 5)

Reorder the terms:
x(1 + x) = 2(x + 5)
(1 * x + x * x) = 2(x + 5)
(1x + x2) = 2(x + 5)

Reorder the terms:
1x + x2 = 2(5 + x)
1x + x2 = (5 * 2 + x * 2)
1x + x2 = (10 + 2x)

Solving
1x + x2 = 10 + 2x

Solving for variable 'x'.

Reorder the terms:
-10 + 1x + -2x + x2 = 10 + 2x + -10 + -2x

Combine like terms: 1x + -2x = -1x
-10 + -1x + x2 = 10 + 2x + -10 + -2x

Reorder the terms:
-10 + -1x + x2 = 10 + -10 + 2x + -2x

Combine like terms: 10 + -10 = 0
-10 + -1x + x2 = 0 + 2x + -2x
-10 + -1x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-10 + -1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -1x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + -1x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1x + x2 = 0 + 10
-1x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
-1x + x2 = 10

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 = 10 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 10 + 0.25

Combine like terms: 10 + 0.25 = 10.25
0.25 + -1x + x2 = 10.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(x + -0.5) equal to 3.201562119 and -3.201562119.

Subproblem 1

x + -0.5 = 3.201562119 Simplifying x + -0.5 = 3.201562119 Reorder the terms: -0.5 + x = 3.201562119 Solving -0.5 + x = 3.201562119 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 = 3.201562119 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 3.201562119 + 0.5 x = 3.201562119 + 0.5 Combine like terms: 3.201562119 + 0.5 = 3.701562119 x = 3.701562119 Simplifying x = 3.701562119

Subproblem 2

x + -0.5 = -3.201562119 Simplifying x + -0.5 = -3.201562119 Reorder the terms: -0.5 + x = -3.201562119 Solving -0.5 + x = -3.201562119 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 = -3.201562119 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -3.201562119 + 0.5 x = -3.201562119 + 0.5 Combine like terms: -3.201562119 + 0.5 = -2.701562119 x = -2.701562119 Simplifying x = -2.701562119

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.701562119, -2.701562119}

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