k^2+35k-9=0

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Solution for k^2+35k-9=0 equation:


Simplifying
k2 + 35k + -9 = 0

Reorder the terms:
-9 + 35k + k2 = 0

Solving
-9 + 35k + k2 = 0

Solving for variable 'k'.

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + 35k + 9 + k2 = 0 + 9

Reorder the terms:
-9 + 9 + 35k + k2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 35k + k2 = 0 + 9
35k + k2 = 0 + 9

Combine like terms: 0 + 9 = 9
35k + k2 = 9

The k term is 35k.  Take half its coefficient (17.5).
Square it (306.25) and add it to both sides.

Add '306.25' to each side of the equation.
35k + 306.25 + k2 = 9 + 306.25

Reorder the terms:
306.25 + 35k + k2 = 9 + 306.25

Combine like terms: 9 + 306.25 = 315.25
306.25 + 35k + k2 = 315.25

Factor a perfect square on the left side:
(k + 17.5)(k + 17.5) = 315.25

Calculate the square root of the right side: 17.755280905

Break this problem into two subproblems by setting 
(k + 17.5) equal to 17.755280905 and -17.755280905.

Subproblem 1

k + 17.5 = 17.755280905 Simplifying k + 17.5 = 17.755280905 Reorder the terms: 17.5 + k = 17.755280905 Solving 17.5 + k = 17.755280905 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-17.5' to each side of the equation. 17.5 + -17.5 + k = 17.755280905 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + k = 17.755280905 + -17.5 k = 17.755280905 + -17.5 Combine like terms: 17.755280905 + -17.5 = 0.255280905 k = 0.255280905 Simplifying k = 0.255280905

Subproblem 2

k + 17.5 = -17.755280905 Simplifying k + 17.5 = -17.755280905 Reorder the terms: 17.5 + k = -17.755280905 Solving 17.5 + k = -17.755280905 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-17.5' to each side of the equation. 17.5 + -17.5 + k = -17.755280905 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + k = -17.755280905 + -17.5 k = -17.755280905 + -17.5 Combine like terms: -17.755280905 + -17.5 = -35.255280905 k = -35.255280905 Simplifying k = -35.255280905

Solution

The solution to the problem is based on the solutions from the subproblems. k = {0.255280905, -35.255280905}

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