Simplifying
100x2 + -100x + 9 = 0
Reorder the terms:
9 + -100x + 100x2 = 0
Solving
9 + -100x + 100x2 = 0
Solving for variable 'x'.
Begin completing the square. Divide all terms by
100 the coefficient of the squared term:
Divide each side by '100'.
0.09 + -1x + x2 = 0
Move the constant term to the right:
Add '-0.09' to each side of the equation.
0.09 + -1x + -0.09 + x2 = 0 + -0.09
Reorder the terms:
0.09 + -0.09 + -1x + x2 = 0 + -0.09
Combine like terms: 0.09 + -0.09 = 0.00
0.00 + -1x + x2 = 0 + -0.09
-1x + x2 = 0 + -0.09
Combine like terms: 0 + -0.09 = -0.09
-1x + x2 = -0.09
The x term is -1x. Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.
Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = -0.09 + 0.25
Reorder the terms:
0.25 + -1x + x2 = -0.09 + 0.25
Combine like terms: -0.09 + 0.25 = 0.16
0.25 + -1x + x2 = 0.16
Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 0.16
Calculate the square root of the right side: 0.4
Break this problem into two subproblems by setting
(x + -0.5) equal to 0.4 and -0.4.
Subproblem 1
x + -0.5 = 0.4
Simplifying
x + -0.5 = 0.4
Reorder the terms:
-0.5 + x = 0.4
Solving
-0.5 + x = 0.4
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 0.4 + 0.5
Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 0.4 + 0.5
x = 0.4 + 0.5
Combine like terms: 0.4 + 0.5 = 0.9
x = 0.9
Simplifying
x = 0.9
Subproblem 2
x + -0.5 = -0.4
Simplifying
x + -0.5 = -0.4
Reorder the terms:
-0.5 + x = -0.4
Solving
-0.5 + x = -0.4
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = -0.4 + 0.5
Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -0.4 + 0.5
x = -0.4 + 0.5
Combine like terms: -0.4 + 0.5 = 0.1
x = 0.1
Simplifying
x = 0.1
Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.9, 0.1}
