factorise. x^2-13x+18=0 by factorisation
Answers
Answer:
Simplifying
x2 + -13x + 18 = 0
Reorder the terms:
18 + -13x + x2 = 0
Solving
18 + -13x + x2 = 0
Solving for variable 'x'.
Begin completing the square.
Move the constant term to the right:
Add '-18' to each side of the equation.
18 + -13x + -18 + x2 = 0 + -18
Reorder the terms:
18 + -18 + -13x + x2 = 0 + -18
Combine like terms: 18 + -18 = 0
0 + -13x + x2 = 0 + -18
-13x + x2 = 0 + -18
Combine like terms: 0 + -18 = -18
-13x + x2 = -18
The x term is -13x. Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.
Add '42.25' to each side of the equation.
-13x + 42.25 + x2 = -18 + 42.25
Reorder the terms:
42.25 + -13x + x2 = -18 + 42.25
Combine like terms: -18 + 42.25 = 24.25
42.25 + -13x + x2 = 24.25
Factor a perfect square on the left side:
(x + -6.5)(x + -6.5) = 24.25
Calculate the square root of the right side: 4.924428901
Break this problem into two subproblems by setting
(x + -6.5) equal to 4.924428901 and -4.924428901.
Subproblem 1
x + -6.5 = 4.924428901
Simplifying
x + -6.5 = 4.924428901
Reorder the terms:
-6.5 + x = 4.924428901
Solving
-6.5 + x = 4.924428901
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '6.5' to each side of the equation.
-6.5 + 6.5 + x = 4.924428901 + 6.5
Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x = 4.924428901 + 6.5
x = 4.924428901 + 6.5
Combine like terms: 4.924428901 + 6.5 = 11.424428901
x = 11.424428901
Simplifying
x = 11.424428901
Subproblem 2
x + -6.5 = -4.924428901
Simplifying
x + -6.5 = -4.924428901
Reorder the terms:
-6.5 + x = -4.924428901
Solving
-6.5 + x = -4.924428901
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '6.5' to each side of the equation.
-6.5 + 6.5 + x = -4.924428901 + 6.5
Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x = -4.924428901 + 6.5
x = -4.924428901 + 6.5
Combine like terms: -4.924428901 + 6.5 = 1.575571099
x = 1.575571099
Simplifying
x = 1.575571099
Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.424428901, 1.575571099}