Sagot :
Answer:
m = {0.372281323, -5.372281323}
Step-by-step explanation:
Simplifying
m2 + 5m + -2 = 0
Reorder the terms:
-2 + 5m + m2 = 0
Solving
-2 + 5m + m2 = 0
Solving for variable 'm'.
Begin completing the square.
Move the constant term to the right:
Add '2' to each side of the equation.
-2 + 5m + 2 + m2 = 0 + 2
Reorder the terms:
-2 + 2 + 5m + m2 = 0 + 2
Combine like terms: -2 + 2 = 0
0 + 5m + m2 = 0 + 2
5m + m2 = 0 + 2
Combine like terms: 0 + 2 = 2
5m + m2 = 2
The m term is 5m. Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.
Add '6.25' to each side of the equation.
5m + 6.25 + m2 = 2 + 6.25
Reorder the terms:
6.25 + 5m + m2 = 2 + 6.25
Combine like terms: 2 + 6.25 = 8.25
6.25 + 5m + m2 = 8.25
Factor a perfect square on the left side:
(m + 2.5)(m + 2.5) = 8.25
Calculate the square root of the right side: 2.872281323
Break this problem into two subproblems by setting
(m + 2.5) equal to 2.872281323 and -2.872281323.
Subproblem 1
m + 2.5 = 2.872281323
Simplifying
m + 2.5 = 2.872281323
Reorder the terms:
2.5 + m = 2.872281323
Solving
2.5 + m = 2.872281323
Solving for variable 'm'.
Move all terms containing m to the left, all other terms to the right.
Add '-2.5' to each side of the equation.
2.5 + -2.5 + m = 2.872281323 + -2.5
Combine like terms: 2.5 + -2.5 = 0.0
0.0 + m = 2.872281323 + -2.5
m = 2.872281323 + -2.5
Combine like terms: 2.872281323 + -2.5 = 0.372281323
m = 0.372281323
Simplifying
m = 0.372281323
Subproblem 2
m + 2.5 = -2.872281323
Simplifying
m + 2.5 = -2.872281323
Reorder the terms:
2.5 + m = -2.872281323
Solving
2.5 + m = -2.872281323
Solving for variable 'm'.
Move all terms containing m to the left, all other terms to the right.
Add '-2.5' to each side of the equation.
2.5 + -2.5 + m = -2.872281323 + -2.5
Combine like terms: 2.5 + -2.5 = 0.0
0.0 + m = -2.872281323 + -2.5
m = -2.872281323 + -2.5
Combine like terms: -2.872281323 + -2.5 = -5.372281323
m = -5.372281323
Simplifying
m = -5.372281323
.