Explanation:
Simplifying
x2 + -9x + -3 = 0
Reorder the terms:
-3 + -9x + x2 = 0
Solving
-3 + -9x + x2 = 0
Solving for variable 'x'.
Begin completing the square.
Move the constant term to the right:
Add '3' to each side of the equation.
-3 + -9x + 3 + x2 = 0 + 3
Reorder the terms:
-3 + 3 + -9x + x2 = 0 + 3
Combine like terms: -3 + 3 = 0
0 + -9x + x2 = 0 + 3
-9x + x2 = 0 + 3
Combine like terms: 0 + 3 = 3
-9x + x2 = 3
The x term is -9x. Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.
Add '20.25' to each side of the equation.
-9x + 20.25 + x2 = 3 + 20.25
Reorder the terms:
20.25 + -9x + x2 = 3 + 20.25
Combine like terms: 3 + 20.25 = 23.25
20.25 + -9x + x2 = 23.25
Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 23.25
Calculate the square root of the right side: 4.82182538
Break this problem into two subproblems by setting
(x + -4.5) equal to 4.82182538 and -4.82182538.
Subproblem 1
x + -4.5 = 4.82182538
Simplifying
x + -4.5 = 4.82182538
Reorder the terms:
-4.5 + x = 4.82182538
Solving
-4.5 + x = 4.82182538
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = 4.82182538 + 4.5
Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = 4.82182538 + 4.5
x = 4.82182538 + 4.5
Combine like terms: 4.82182538 + 4.5 = 9.32182538
x = 9.32182538
Simplifying
x = 9.32182538
Subproblem 2
x + -4.5 = -4.82182538
Simplifying
x + -4.5 = -4.82182538
Reorder the terms:
-4.5 + x = -4.82182538
Solving
-4.5 + x = -4.82182538
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = -4.82182538 + 4.5
Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = -4.82182538 + 4.5
x = -4.82182538 + 4.5
Combine like terms: -4.82182538 + 4.5 = -0.32182538
x = -0.32182538
Simplifying
x = -0.32182538
Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.32182538, -0.32182538}