x^2+2(2k+5)x-(13k+4)=0

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Solution for x^2+2(2k+5)x-(13k+4)=0 equation: 


Simplifying
x2 + 2(2k + 5) * x + -1(13k + 4) = 0

Reorder the terms:
x2 + 2(5 + 2k) * x + -1(13k + 4) = 0

Reorder the terms for easier multiplication:
x2 + 2x(5 + 2k) + -1(13k + 4) = 0
x2 + (5 * 2x + 2k * 2x) + -1(13k + 4) = 0

Reorder the terms:
x2 + (4kx + 10x) + -1(13k + 4) = 0
x2 + (4kx + 10x) + -1(13k + 4) = 0

Reorder the terms:
x2 + 4kx + 10x + -1(4 + 13k) = 0
x2 + 4kx + 10x + (4 * -1 + 13k * -1) = 0
x2 + 4kx + 10x + (-4 + -13k) = 0

Reorder the terms:
-4 + -13k + 4kx + 10x + x2 = 0

Solving
-4 + -13k + 4kx + 10x + x2 = 0

Solving for variable 'k'.

Move all terms containing k to the left, all other terms to the right.

Add '4' to each side of the equation.
-4 + -13k + 4kx + 10x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + -13k + 4kx + 10x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -13k + 4kx + 10x + x2 = 0 + 4
-13k + 4kx + 10x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
-13k + 4kx + 10x + x2 = 4

Add '-10x' to each side of the equation.
-13k + 4kx + 10x + -10x + x2 = 4 + -10x

Combine like terms: 10x + -10x = 0
-13k + 4kx + 0 + x2 = 4 + -10x
-13k + 4kx + x2 = 4 + -10x

Add '-1x2' to each side of the equation.
-13k + 4kx + x2 + -1x2 = 4 + -10x + -1x2

Combine like terms: x2 + -1x2 = 0
-13k + 4kx + 0 = 4 + -10x + -1x2
-13k + 4kx = 4 + -10x + -1x2

Reorder the terms:
-4 + -13k + 4kx + 10x + x2 = 4 + -10x + -1x2 + -4 + 10x + x2

Reorder the terms:
-4 + -13k + 4kx + 10x + x2 = 4 + -4 + -10x + 10x + -1x2 + x2

Combine like terms: 4 + -4 = 0
-4 + -13k + 4kx + 10x + x2 = 0 + -10x + 10x + -1x2 + x2
-4 + -13k + 4kx + 10x + x2 = -10x + 10x + -1x2 + x2

Combine like terms: -10x + 10x = 0
-4 + -13k + 4kx + 10x + x2 = 0 + -1x2 + x2
-4 + -13k + 4kx + 10x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-4 + -13k + 4kx + 10x + x2 = 0

The solution to this equation could not be determined.

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