k²-8k+16 solution kailangan ko lang po hehe
Answer:
k²-8k+16= 28
Step-by-step explanation:
Simplifying
k2 + 8k + 16 = 28
Reorder the terms:
16 + 8k + k2 = 28
Solving
16 + 8k + k2 = 28
Solving for variable ‘k’.
Reorder the terms:
16 + -28 + 8k + k2 = 28 + -28
Combine like terms: 16 + -28 = -12
-12 + 8k + k2 = 28 + -28
Combine like terms: 28 + -28 = 0
-12 + 8k + k2 = 0
Begin completing the square.
Move the constant term to the right:
Add ’12’ to each side of the equation.
-12 + 8k + 12 + k2 = 0 + 12
Reorder the terms:
-12 + 12 + 8k + k2 = 0 + 12
Combine like terms: -12 + 12 = 0
0 + 8k + k2 = 0 + 12
8k + k2 = 0 + 12
Combine like terms: 0 + 12 = 12
8k + k2 = 12
The k term is 8k. Take half its coefficient (4).
Square it (16) and add it to both sides.
Add ’16’ to each side of the equation.
8k + 16 + k2 = 12 + 16
Reorder the terms:
16 + 8k + k2 = 12 + 16
Combine like terms: 12 + 16 = 28
16 + 8k + k2 = 28
Factor a perfect square on the left side:
(k + 4)(k + 4) = 28
Calculate the square root of the right side: 5.291502622
Break this problem into two subproblems by setting
(k + 4) equal to 5.291502622 and -5.291502622.
Subproblem 1
k + 4 = 5.291502622
Simplifying
k + 4 = 5.291502622
Reorder the terms:
4 + k = 5.291502622
Solving
4 + k = 5.291502622
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 + -4 + k = 5.291502622 + -4
Combine like terms: 4 + -4 = 0
0 + k = 5.291502622 + -4
k = 5.291502622 + -4
Combine like terms: 5.291502622 + -4 = 1.291502622
k = 1.291502622
Simplifying
k = 1.291502622
Subproblem 2
k + 4 = -5.291502622
Simplifying
k + 4 = -5.291502622
Reorder the terms:
4 + k = -5.291502622
Solving
4 + k = -5.291502622
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 + -4 + k = -5.291502622 + -4
Combine like terms: 4 + -4 = 0
0 + k = -5.291502622 + -4
k = -5.291502622 + -4
Combine like terms: -5.291502622 + -4 = -9.291502622
k = -9.291502622
Simplifying
k = -9.291502622
Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {1.291502622, -9.291502622}
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