Answer:
Step-by-step explanation:Simplifying
x2 + -9x = 4x + -4
Reorder the terms:
-9x + x2 = 4x + -4
Reorder the terms:
-9x + x2 = -4 + 4x
Solving
-9x + x2 = -4 + 4x
Solving for variable 'x'.
Reorder the terms:
4 + -9x + -4x + x2 = -4 + 4x + 4 + -4x
Combine like terms: -9x + -4x = -13x
4 + -13x + x2 = -4 + 4x + 4 + -4x
Reorder the terms:
4 + -13x + x2 = -4 + 4 + 4x + -4x
Combine like terms: -4 + 4 = 0
4 + -13x + x2 = 0 + 4x + -4x
4 + -13x + x2 = 4x + -4x
Combine like terms: 4x + -4x = 0
4 + -13x + x2 = 0
Begin completing the square.
Move the constant term to the right:
Add '-4' to each side of the equation.
4 + -13x + -4 + x2 = 0 + -4
Reorder the terms:
4 + -4 + -13x + x2 = 0 + -4
Combine like terms: 4 + -4 = 0
0 + -13x + x2 = 0 + -4
-13x + x2 = 0 + -4
Combine like terms: 0 + -4 = -4
-13x + x2 = -4
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 = -4 + 42.25
Reorder the terms:
42.25 + -13x + x2 = -4 + 42.25
Combine like terms: -4 + 42.25 = 38.25
42.25 + -13x + x2 = 38.25
Factor a perfect square on the left side:
(x + -6.5)(x + -6.5) = 38.25
Calculate the square root of the right side: 6.184658438
Break this problem into two subproblems by setting
(x + -6.5) equal to 6.184658438 and -6.184658438.
