17=2x(x+5)

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Solution for 17=2x(x+5) equation:


Simplifying
17 = 2x(x + 5)

Reorder the terms:
17 = 2x(5 + x)
17 = (5 * 2x + x * 2x)
17 = (10x + 2x2)

Solving
17 = 10x + 2x2

Solving for variable 'x'.

Reorder the terms:
17 + -10x + -2x2 = 10x + -10x + 2x2 + -2x2

Combine like terms: 10x + -10x = 0
17 + -10x + -2x2 = 0 + 2x2 + -2x2
17 + -10x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
17 + -10x + -2x2 = 0

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

Divide each side by '-2'.
-8.5 + 5x + x2 = 0

Move the constant term to the right:

Add '8.5' to each side of the equation.
-8.5 + 5x + 8.5 + x2 = 0 + 8.5

Reorder the terms:
-8.5 + 8.5 + 5x + x2 = 0 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + 5x + x2 = 0 + 8.5
5x + x2 = 0 + 8.5

Combine like terms: 0 + 8.5 = 8.5
5x + x2 = 8.5

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 8.5 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 8.5 + 6.25

Combine like terms: 8.5 + 6.25 = 14.75
6.25 + 5x + x2 = 14.75

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 14.75

Calculate the square root of the right side: 3.840572874

Break this problem into two subproblems by setting 
(x + 2.5) equal to 3.840572874 and -3.840572874.

Subproblem 1

x + 2.5 = 3.840572874 Simplifying x + 2.5 = 3.840572874 Reorder the terms: 2.5 + x = 3.840572874 Solving 2.5 + x = 3.840572874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 3.840572874 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 3.840572874 + -2.5 x = 3.840572874 + -2.5 Combine like terms: 3.840572874 + -2.5 = 1.340572874 x = 1.340572874 Simplifying x = 1.340572874

Subproblem 2

x + 2.5 = -3.840572874 Simplifying x + 2.5 = -3.840572874 Reorder the terms: 2.5 + x = -3.840572874 Solving 2.5 + x = -3.840572874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -3.840572874 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -3.840572874 + -2.5 x = -3.840572874 + -2.5 Combine like terms: -3.840572874 + -2.5 = -6.340572874 x = -6.340572874 Simplifying x = -6.340572874

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.340572874, -6.340572874}

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