Simplifying
x2 = 0.6x + -0.08
Reorder the terms:
x2 = -0.08 + 0.6x
Solving
x2 = -0.08 + 0.6x
Solving for variable 'x'.
Reorder the terms:
0.08 + -0.6x + x2 = -0.08 + 0.6x + 0.08 + -0.6x
Reorder the terms:
0.08 + -0.6x + x2 = -0.08 + 0.08 + 0.6x + -0.6x
Combine like terms: -0.08 + 0.08 = 0.00
0.08 + -0.6x + x2 = 0.00 + 0.6x + -0.6x
0.08 + -0.6x + x2 = 0.6x + -0.6x
Combine like terms: 0.6x + -0.6x = 0.0
0.08 + -0.6x + x2 = 0.0
Begin completing the square.
Move the constant term to the right:
Add '-0.08' to each side of the equation.
0.08 + -0.6x + -0.08 + x2 = 0.0 + -0.08
Reorder the terms:
0.08 + -0.08 + -0.6x + x2 = 0.0 + -0.08
Combine like terms: 0.08 + -0.08 = 0.00
0.00 + -0.6x + x2 = 0.0 + -0.08
-0.6x + x2 = 0.0 + -0.08
Combine like terms: 0.0 + -0.08 = -0.08
-0.6x + x2 = -0.08
The x term is -0.6x. Take half its coefficient (-0.3).
Square it (0.09) and add it to both sides.
Add '0.09' to each side of the equation.
-0.6x + 0.09 + x2 = -0.08 + 0.09
Reorder the terms:
0.09 + -0.6x + x2 = -0.08 + 0.09
Combine like terms: -0.08 + 0.09 = 0.01
0.09 + -0.6x + x2 = 0.01
Factor a perfect square on the left side:
(x + -0.3)(x + -0.3) = 0.01
Calculate the square root of the right side: 0.1
Break this problem into two subproblems by setting
(x + -0.3) equal to 0.1 and -0.1.
Subproblem 1
x + -0.3 = 0.1
Simplifying
x + -0.3 = 0.1
Reorder the terms:
-0.3 + x = 0.1
Solving
-0.3 + x = 0.1
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '0.3' to each side of the equation.
-0.3 + 0.3 + x = 0.1 + 0.3
Combine like terms: -0.3 + 0.3 = 0.0
0.0 + x = 0.1 + 0.3
x = 0.1 + 0.3
Combine like terms: 0.1 + 0.3 = 0.4
x = 0.4
Simplifying
x = 0.4
Subproblem 2
x + -0.3 = -0.1
Simplifying
x + -0.3 = -0.1
Reorder the terms:
-0.3 + x = -0.1
Solving
-0.3 + x = -0.1
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '0.3' to each side of the equation.
-0.3 + 0.3 + x = -0.1 + 0.3
Combine like terms: -0.3 + 0.3 = 0.0
0.0 + x = -0.1 + 0.3
x = -0.1 + 0.3
Combine like terms: -0.1 + 0.3 = 0.2
x = 0.2
Simplifying
x = 0.2
Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.4, 0.2}
