x^2-17x-30=

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Solution for x^2-17x-30= equation:


Simplifying
x2 + -17x + -30 = 0

Reorder the terms:
-30 + -17x + x2 = 0

Solving
-30 + -17x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + -17x + 30 + x2 = 0 + 30

Reorder the terms:
-30 + 30 + -17x + x2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + -17x + x2 = 0 + 30
-17x + x2 = 0 + 30

Combine like terms: 0 + 30 = 30
-17x + x2 = 30

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 = 30 + 72.25

Reorder the terms:
72.25 + -17x + x2 = 30 + 72.25

Combine like terms: 30 + 72.25 = 102.25
72.25 + -17x + x2 = 102.25

Factor a perfect square on the left side:
(x + -8.5)(x + -8.5) = 102.25

Calculate the square root of the right side: 10.111874208

Break this problem into two subproblems by setting 
(x + -8.5) equal to 10.111874208 and -10.111874208.

Subproblem 1

x + -8.5 = 10.111874208 Simplifying x + -8.5 = 10.111874208 Reorder the terms: -8.5 + x = 10.111874208 Solving -8.5 + x = 10.111874208 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 = 10.111874208 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 10.111874208 + 8.5 x = 10.111874208 + 8.5 Combine like terms: 10.111874208 + 8.5 = 18.611874208 x = 18.611874208 Simplifying x = 18.611874208

Subproblem 2

x + -8.5 = -10.111874208 Simplifying x + -8.5 = -10.111874208 Reorder the terms: -8.5 + x = -10.111874208 Solving -8.5 + x = -10.111874208 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 = -10.111874208 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -10.111874208 + 8.5 x = -10.111874208 + 8.5 Combine like terms: -10.111874208 + 8.5 = -1.611874208 x = -1.611874208 Simplifying x = -1.611874208

Solution

The solution to the problem is based on the solutions from the subproblems. x = {18.611874208, -1.611874208}

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