1x^2+2x-17=0

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Solution for 1x^2+2x-17=0 equation:


Simplifying
1x2 + 2x + -17 = 0

Reorder the terms:
-17 + 2x + 1x2 = 0

Solving
-17 + 2x + 1x2 = 0

Solving for variable 'x'.

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 = 3.242640687 x = 3.242640687 Simplifying x = 3.242640687

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 = -5.242640687 x = -5.242640687 Simplifying x = -5.242640687

Solution

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

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