0=(k*k)-12k+35

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Solution for 0=(k*k)-12k+35 equation:


Simplifying
0 = (k * k) + -12k + 35

Multiply k * k
0 = (k2) + -12k + 35
0 = k2 + -12k + 35

Reorder the terms:
0 = 35 + -12k + k2

Solving
0 = 35 + -12k + k2

Solving for variable 'k'.

Combine like terms: 0 + -35 = -35
-35 + 12k + -1k2 = 35 + -12k + k2 + -35 + 12k + -1k2

Reorder the terms:
-35 + 12k + -1k2 = 35 + -35 + -12k + 12k + k2 + -1k2

Combine like terms: 35 + -35 = 0
-35 + 12k + -1k2 = 0 + -12k + 12k + k2 + -1k2
-35 + 12k + -1k2 = -12k + 12k + k2 + -1k2

Combine like terms: -12k + 12k = 0
-35 + 12k + -1k2 = 0 + k2 + -1k2
-35 + 12k + -1k2 = k2 + -1k2

Combine like terms: k2 + -1k2 = 0
-35 + 12k + -1k2 = 0

Factor a trinomial.
(-7 + k)(5 + -1k) = 0

Subproblem 1

Set the factor '(-7 + k)' equal to zero and attempt to solve: Simplifying -7 + k = 0 Solving -7 + k = 0 Move all terms containing k to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + k = 0 + 7 Combine like terms: -7 + 7 = 0 0 + k = 0 + 7 k = 0 + 7 Combine like terms: 0 + 7 = 7 k = 7 Simplifying k = 7

Subproblem 2

Set the factor '(5 + -1k)' equal to zero and attempt to solve: Simplifying 5 + -1k = 0 Solving 5 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1k = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1k = 0 + -5 -1k = 0 + -5 Combine like terms: 0 + -5 = -5 -1k = -5 Divide each side by '-1'. k = 5 Simplifying k = 5

Solution

k = {7, 5}

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