0=x^2+34x-165

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Solution for 0=x^2+34x-165 equation:


Simplifying
0 = x2 + 34x + -165

Reorder the terms:
0 = -165 + 34x + x2

Solving
0 = -165 + 34x + x2

Solving for variable 'x'.

Combine like terms: 0 + 165 = 165
165 + -34x + -1x2 = -165 + 34x + x2 + 165 + -34x + -1x2

Reorder the terms:
165 + -34x + -1x2 = -165 + 165 + 34x + -34x + x2 + -1x2

Combine like terms: -165 + 165 = 0
165 + -34x + -1x2 = 0 + 34x + -34x + x2 + -1x2
165 + -34x + -1x2 = 34x + -34x + x2 + -1x2

Combine like terms: 34x + -34x = 0
165 + -34x + -1x2 = 0 + x2 + -1x2
165 + -34x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
165 + -34x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-165 + 34x + x2 = 0

Move the constant term to the right:

Add '165' to each side of the equation.
-165 + 34x + 165 + x2 = 0 + 165

Reorder the terms:
-165 + 165 + 34x + x2 = 0 + 165

Combine like terms: -165 + 165 = 0
0 + 34x + x2 = 0 + 165
34x + x2 = 0 + 165

Combine like terms: 0 + 165 = 165
34x + x2 = 165

The x term is 34x.  Take half its coefficient (17).
Square it (289) and add it to both sides.

Add '289' to each side of the equation.
34x + 289 + x2 = 165 + 289

Reorder the terms:
289 + 34x + x2 = 165 + 289

Combine like terms: 165 + 289 = 454
289 + 34x + x2 = 454

Factor a perfect square on the left side:
(x + 17)(x + 17) = 454

Calculate the square root of the right side: 21.307275753

Break this problem into two subproblems by setting 
(x + 17) equal to 21.307275753 and -21.307275753.

Subproblem 1

x + 17 = 21.307275753 Simplifying x + 17 = 21.307275753 Reorder the terms: 17 + x = 21.307275753 Solving 17 + x = 21.307275753 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + x = 21.307275753 + -17 Combine like terms: 17 + -17 = 0 0 + x = 21.307275753 + -17 x = 21.307275753 + -17 Combine like terms: 21.307275753 + -17 = 4.307275753 x = 4.307275753 Simplifying x = 4.307275753

Subproblem 2

x + 17 = -21.307275753 Simplifying x + 17 = -21.307275753 Reorder the terms: 17 + x = -21.307275753 Solving 17 + x = -21.307275753 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + x = -21.307275753 + -17 Combine like terms: 17 + -17 = 0 0 + x = -21.307275753 + -17 x = -21.307275753 + -17 Combine like terms: -21.307275753 + -17 = -38.307275753 x = -38.307275753 Simplifying x = -38.307275753

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.307275753, -38.307275753}

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