x² - 12x + 9 (Factorize)
Answers
Answer:
Simplifying
x2 + -12x + 9 = 0
Reorder the terms:
9 + -12x + x2 = 0
Solving
9 + -12x + x2 = 0
Solving for variable 'x'.
Begin completing the square.
Move the constant term to the right:
Add '-9' to each side of the equation.
9 + -12x + -9 + x2 = 0 + -9
Reorder the terms:
9 + -9 + -12x + x2 = 0 + -9
Combine like terms: 9 + -9 = 0
0 + -12x + x2 = 0 + -9
-12x + x2 = 0 + -9
Combine like terms: 0 + -9 = -9
-12x + x2 = -9
The x term is -12x. Take half its coefficient (-6).
Square it (36) and add it to both sides.
Add '36' to each side of the equation.
-12x + 36 + x2 = -9 + 36
Reorder the terms:
36 + -12x + x2 = -9 + 36
Combine like terms: -9 + 36 = 27
36 + -12x + x2 = 27
Factor a perfect square on the left side:
(x + -6)(x + -6) = 27
Calculate the square root of the right side: 5.196152423
Break this problem into two subproblems by setting
(x + -6) equal to 5.196152423 and -5.196152423.
Subproblem 1
x + -6 = 5.196152423
Simplifying
x + -6 = 5.196152423
Reorder the terms:
-6 + x = 5.196152423
Solving
-6 + x = 5.196152423
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '6' to each side of the equation.
-6 + 6 + x = 5.196152423 + 6
Combine like terms: -6 + 6 = 0
0 + x = 5.196152423 + 6
x = 5.196152423 + 6
Combine like terms: 5.196152423 + 6 = 11.196152423
x = 11.196152423
Simplifying
x = 11.196152423
Subproblem 2
x + -6 = -5.196152423
Simplifying
x + -6 = -5.196152423
Reorder the terms:
-6 + x = -5.196152423
Solving
-6 + x = -5.196152423
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '6' to each side of the equation.
-6 + 6 + x = -5.196152423 + 6
Combine like terms: -6 + 6 = 0
0 + x = -5.196152423 + 6
x = -5.196152423 + 6
Combine like terms: -5.196152423 + 6 = 0.803847577
x = 0.803847577
Simplifying
x = 0.803847577
Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.196152423, 0.803847577}
.
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Answer:
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