1.7(1.7)=x(x+2)

Solution for 1.7(1.7)=x(x+2) equation:

Simplifying
1.7(1.7) = x(x + 2)

Multiply 1.7 * 1.7
2.89 = x(x + 2)

Reorder the terms:
2.89 = x(2 + x)
2.89 = (2 * x + x * x)
2.89 = (2x + x2)

Solving
2.89 = 2x + x2

Solving for variable 'x'.

Reorder the terms:
2.89 + -2x + -1x2 = 2x + -2x + x2 + -1x2

Combine like terms: 2x + -2x = 0
2.89 + -2x + -1x2 = 0 + x2 + -1x2
2.89 + -2x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
2.89 + -2x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-2.89 + 2x + x2 = 0

Move the constant term to the right:

Add '2.89' to each side of the equation.
-2.89 + 2x + 2.89 + x2 = 0 + 2.89

Reorder the terms:
-2.89 + 2.89 + 2x + x2 = 0 + 2.89

Combine like terms: -2.89 + 2.89 = 0.00
0.00 + 2x + x2 = 0 + 2.89
2x + x2 = 0 + 2.89

Combine like terms: 0 + 2.89 = 2.89
2x + x2 = 2.89

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 2.89 + 1

Reorder the terms:
1 + 2x + x2 = 2.89 + 1

Combine like terms: 2.89 + 1 = 3.89
1 + 2x + x2 = 3.89

Factor a perfect square on the left side:
(x + 1)(x + 1) = 3.89

Calculate the square root of the right side: 1.972308292

Break this problem into two subproblems by setting 
(x + 1) equal to 1.972308292 and -1.972308292.

Subproblem 1
x + 1 = 1.972308292

Simplifying
x + 1 = 1.972308292

Reorder the terms:
1 + x = 1.972308292

Solving
1 + x = 1.972308292

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 1.972308292 + -1

Combine like terms: 1 + -1 = 0
0 + x = 1.972308292 + -1
x = 1.972308292 + -1

Combine like terms: 1.972308292 + -1 = 0.972308292
x = 0.972308292

Simplifying
x = 0.972308292

Subproblem 2
x + 1 = -1.972308292

Simplifying
x + 1 = -1.972308292

Reorder the terms:
1 + x = -1.972308292

Solving
1 + x = -1.972308292

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -1.972308292 + -1

Combine like terms: 1 + -1 = 0
0 + x = -1.972308292 + -1
x = -1.972308292 + -1

Combine like terms: -1.972308292 + -1 = -2.972308292
x = -2.972308292

Simplifying
x = -2.972308292

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.972308292, -2.972308292}