factorise x^2-2x-33
Answers
Answer:
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Answer:
x2 + 2x + -33 = 0
Reorder the terms:
-33 + 2x + x2 = 0
Solving
-33 + 2x + x2 = 0
Solving for variable 'x'.
Begin completing the square.
Move the constant term to the right:
Add '33' to each side of the equation.
-33 + 2x + 33 + x2 = 0 + 33
Reorder the terms:
-33 + 33 + 2x + x2 = 0 + 33
Combine like terms: -33 + 33 = 0
0 + 2x + x2 = 0 + 33
2x + x2 = 0 + 33
Combine like terms: 0 + 33 = 33
2x + x2 = 33
The x term is 2x. Take half its coefficient (1).
Square it (1) and add it to both sides.
Add '1' to each side of the equation.
2x + 1 + x2 = 33 + 1
Reorder the terms:
1 + 2x + x2 = 33 + 1
Combine like terms: 33 + 1 = 34
1 + 2x + x2 = 34
Factor a perfect square on the left side:
(x + 1)(x + 1) = 34
Calculate the square root of the right side: 5.830951895
Break this problem into two subproblems by setting
(x + 1) equal to 5.830951895 and -5.830951895.
Subproblem 1
x + 1 = 5.830951895
Simplifying
x + 1 = 5.830951895
Reorder the terms:
1 + x = 5.830951895
Solving
1 + x = 5.830951895
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-1' to each side of the equation.
1 + -1 + x = 5.830951895 + -1
Combine like terms: 1 + -1 = 0
0 + x = 5.830951895 + -1
x = 5.830951895 + -1
Combine like terms: 5.830951895 + -1 = 4.830951895
x = 4.830951895
Simplifying
x = 4.830951895
Subproblem 2
x + 1 = -5.830951895
Simplifying
x + 1 = -5.830951895
Reorder the terms:
1 + x = -5.830951895
Solving
1 + x = -5.830951895
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-1' to each side of the equation.
1 + -1 + x = -5.830951895 + -1
Combine like terms: 1 + -1 = 0
0 + x = -5.830951895 + -1
x = -5.830951895 + -1
Combine like terms: -5.830951895 + -1 = -6.830951895
x = -6.830951895
Simplifying
x = -6.830951895
Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.830951895, -6.830951895}