Simplifying
18m2 + 6m + 6 = 6m2 + 30m + -3
Reorder the terms:
6 + 6m + 18m2 = 6m2 + 30m + -3
Reorder the terms:
6 + 6m + 18m2 = -3 + 30m + 6m2
Solving
6 + 6m + 18m2 = -3 + 30m + 6m2
Solving for variable 'm'.
Reorder the terms:
6 + 3 + 6m + -30m + 18m2 + -6m2 = -3 + 30m + 6m2 + 3 + -30m + -6m2
Combine like terms: 6 + 3 = 9
9 + 6m + -30m + 18m2 + -6m2 = -3 + 30m + 6m2 + 3 + -30m + -6m2
Combine like terms: 6m + -30m = -24m
9 + -24m + 18m2 + -6m2 = -3 + 30m + 6m2 + 3 + -30m + -6m2
Combine like terms: 18m2 + -6m2 = 12m2
9 + -24m + 12m2 = -3 + 30m + 6m2 + 3 + -30m + -6m2
Reorder the terms:
9 + -24m + 12m2 = -3 + 3 + 30m + -30m + 6m2 + -6m2
Combine like terms: -3 + 3 = 0
9 + -24m + 12m2 = 0 + 30m + -30m + 6m2 + -6m2
9 + -24m + 12m2 = 30m + -30m + 6m2 + -6m2
Combine like terms: 30m + -30m = 0
9 + -24m + 12m2 = 0 + 6m2 + -6m2
9 + -24m + 12m2 = 6m2 + -6m2
Combine like terms: 6m2 + -6m2 = 0
9 + -24m + 12m2 = 0
Factor out the Greatest Common Factor (GCF), '3'.
3(3 + -8m + 4m2) = 0
Ignore the factor 3.
Subproblem 1
Set the factor '(3 + -8m + 4m2)' equal to zero and attempt to solve:
Simplifying
3 + -8m + 4m2 = 0
Solving
3 + -8m + 4m2 = 0
Begin completing the square. Divide all terms by
4 the coefficient of the squared term:
Divide each side by '4'.
0.75 + -2m + m2 = 0
Move the constant term to the right:
Add '-0.75' to each side of the equation.
0.75 + -2m + -0.75 + m2 = 0 + -0.75
Reorder the terms:
0.75 + -0.75 + -2m + m2 = 0 + -0.75
Combine like terms: 0.75 + -0.75 = 0.00
0.00 + -2m + m2 = 0 + -0.75
-2m + m2 = 0 + -0.75
Combine like terms: 0 + -0.75 = -0.75
-2m + m2 = -0.75
The m term is -2m. Take half its coefficient (-1).
Square it (1) and add it to both sides.
Add '1' to each side of the equation.
-2m + 1 + m2 = -0.75 + 1
Reorder the terms:
1 + -2m + m2 = -0.75 + 1
Combine like terms: -0.75 + 1 = 0.25
1 + -2m + m2 = 0.25
Factor a perfect square on the left side:
(m + -1)(m + -1) = 0.25
Calculate the square root of the right side: 0.5
Break this problem into two subproblems by setting
(m + -1) equal to 0.5 and -0.5.
Subproblem 1
m + -1 = 0.5
Simplifying
m + -1 = 0.5
Reorder the terms:
-1 + m = 0.5
Solving
-1 + m = 0.5
Solving for variable 'm'.
Move all terms containing m to the left, all other terms to the right.
Add '1' to each side of the equation.
-1 + 1 + m = 0.5 + 1
Combine like terms: -1 + 1 = 0
0 + m = 0.5 + 1
m = 0.5 + 1
Combine like terms: 0.5 + 1 = 1.5
m = 1.5
Simplifying
m = 1.5
Subproblem 2
m + -1 = -0.5
Simplifying
m + -1 = -0.5
Reorder the terms:
-1 + m = -0.5
Solving
-1 + m = -0.5
Solving for variable 'm'.
Move all terms containing m to the left, all other terms to the right.
Add '1' to each side of the equation.
-1 + 1 + m = -0.5 + 1
Combine like terms: -1 + 1 = 0
0 + m = -0.5 + 1
m = -0.5 + 1
Combine like terms: -0.5 + 1 = 0.5
m = 0.5
Simplifying
m = 0.5
Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {1.5, 0.5}Solution
m = {1.5, 0.5}
