x^2-17x+4=0

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Solution for x^2-17x+4=0 equation:


Simplifying
x2 + -17x + 4 = 0

Reorder the terms:
4 + -17x + x2 = 0

Solving
4 + -17x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -17x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + -17x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -17x + x2 = 0 + -4
-17x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
-17x + x2 = -4

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 = -4 + 72.25

Reorder the terms:
72.25 + -17x + x2 = -4 + 72.25

Combine like terms: -4 + 72.25 = 68.25
72.25 + -17x + x2 = 68.25

Factor a perfect square on the left side:
(x + -8.5)(x + -8.5) = 68.25

Calculate the square root of the right side: 8.261355821

Break this problem into two subproblems by setting 
(x + -8.5) equal to 8.261355821 and -8.261355821.

Subproblem 1

x + -8.5 = 8.261355821 Simplifying x + -8.5 = 8.261355821 Reorder the terms: -8.5 + x = 8.261355821 Solving -8.5 + x = 8.261355821 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 = 8.261355821 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 8.261355821 + 8.5 x = 8.261355821 + 8.5 Combine like terms: 8.261355821 + 8.5 = 16.761355821 x = 16.761355821 Simplifying x = 16.761355821

Subproblem 2

x + -8.5 = -8.261355821 Simplifying x + -8.5 = -8.261355821 Reorder the terms: -8.5 + x = -8.261355821 Solving -8.5 + x = -8.261355821 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 = -8.261355821 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -8.261355821 + 8.5 x = -8.261355821 + 8.5 Combine like terms: -8.261355821 + 8.5 = 0.238644179 x = 0.238644179 Simplifying x = 0.238644179

Solution

The solution to the problem is based on the solutions from the subproblems. x = {16.761355821, 0.238644179}

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