x^2=17+2x

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Solution for x^2=17+2x equation:


Simplifying
x2 = 17 + 2x

Solving
x2 = 17 + 2x

Solving for variable 'x'.

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

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

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

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

Begin completing the square.

Move the constant term to the right:

Add '17' to each side of the equation.
-17 + -2x + 17 + x2 = 0 + 17

Reorder the terms:
-17 + 17 + -2x + x2 = 0 + 17

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

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

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 = 17 + 1

Reorder the terms:
1 + -2x + x2 = 17 + 1

Combine like terms: 17 + 1 = 18
1 + -2x + x2 = 18

Factor a perfect square on the left side:
(x + -1)(x + -1) = 18

Calculate the square root of the right side: 4.242640687

Break this problem into two subproblems by setting 
(x + -1) equal to 4.242640687 and -4.242640687.

Subproblem 1

x + -1 = 4.242640687 Simplifying x + -1 = 4.242640687 Reorder the terms: -1 + x = 4.242640687 Solving -1 + x = 4.242640687 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 = 4.242640687 + 1 Combine like terms: -1 + 1 = 0 0 + x = 4.242640687 + 1 x = 4.242640687 + 1 Combine like terms: 4.242640687 + 1 = 5.242640687 x = 5.242640687 Simplifying x = 5.242640687

Subproblem 2

x + -1 = -4.242640687 Simplifying x + -1 = -4.242640687 Reorder the terms: -1 + x = -4.242640687 Solving -1 + x = -4.242640687 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 = -4.242640687 + 1 Combine like terms: -1 + 1 = 0 0 + x = -4.242640687 + 1 x = -4.242640687 + 1 Combine like terms: -4.242640687 + 1 = -3.242640687 x = -3.242640687 Simplifying x = -3.242640687

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.242640687, -3.242640687}

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