x^2-17x+18=0

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Solution for x^2-17x+18=0 equation:


Simplifying
x2 + -17x + 18 = 0

Reorder the terms:
18 + -17x + x2 = 0

Solving
18 + -17x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-18' to each side of the equation.
18 + -17x + -18 + x2 = 0 + -18

Reorder the terms:
18 + -18 + -17x + x2 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -17x + x2 = 0 + -18
-17x + x2 = 0 + -18

Combine like terms: 0 + -18 = -18
-17x + x2 = -18

The x term is -17x.  Take half its coefficient (-8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
-17x + 72.25 + x2 = -18 + 72.25

Reorder the terms:
72.25 + -17x + x2 = -18 + 72.25

Combine like terms: -18 + 72.25 = 54.25
72.25 + -17x + x2 = 54.25

Factor a perfect square on the left side:
(x + -8.5)(x + -8.5) = 54.25

Calculate the square root of the right side: 7.365459931

Break this problem into two subproblems by setting 
(x + -8.5) equal to 7.365459931 and -7.365459931.

Subproblem 1

x + -8.5 = 7.365459931 Simplifying x + -8.5 = 7.365459931 Reorder the terms: -8.5 + x = 7.365459931 Solving -8.5 + x = 7.365459931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = 7.365459931 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 7.365459931 + 8.5 x = 7.365459931 + 8.5 Combine like terms: 7.365459931 + 8.5 = 15.865459931 x = 15.865459931 Simplifying x = 15.865459931

Subproblem 2

x + -8.5 = -7.365459931 Simplifying x + -8.5 = -7.365459931 Reorder the terms: -8.5 + x = -7.365459931 Solving -8.5 + x = -7.365459931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = -7.365459931 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -7.365459931 + 8.5 x = -7.365459931 + 8.5 Combine like terms: -7.365459931 + 8.5 = 1.134540069 x = 1.134540069 Simplifying x = 1.134540069

Solution

The solution to the problem is based on the solutions from the subproblems. x = {15.865459931, 1.134540069}

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