<span>Simplifying:
2x2 + -8x + -90 = 0
Reorder the terms:
-90 + -8x + 2x2 = 0
Solving
-90 + -8x + 2x2 = 0
Solving for variable 'x'.
Factor out the Greatest Common Factor (GCF), '2'.
2(-45 + -4x + x2) = 0
Factor a trinomial.
2((-5 + -1x)(9 + -1x)) = 0
Ignore the factor 2.
Subproblem 1:
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:
Simplifying
-5 + -1x = 0
Solving
-5 + -1x = 0
Move all terms containing x to the left, all other terms to the right.
Add '5' to each side of the equation.
-5 + 5 + -1x = 0 + 5
Combine like terms:
-5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5
Combine like terms:
0 + 5 = 5
-1x = 5
Divide each side by '-1'.
x = -5
Simplifying
x = -5
Subproblem 2:
Set the factor '(9 + -1x)' equal to zero and attempt to solve:
Simplifying
9 + -1x = 0
Solving
9 + -1x = 0
Move all terms containing x to the left, all other terms to the right.
Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9
Combine like terms:
9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9
Combine like terms:
0 + -9 = -9
-1x = -9
Divide each side by '-1'.
x = 9
Simplifying
x = 9
Solution
x = {-5, 9}</span>
Answer: The required solution is
Step-by-step explanation: We are given to solve the following differential equation :
Let us consider that
be an auxiliary solution of equation (i).
Then, we have
Substituting these values in equation (i), we get
![m^2e^{mt}+10me^{mt}+25e^{mt}=0\\\\\Rightarrow (m^2+10y+25)e^{mt}=0\\\\\Rightarrow m^2+10m+25=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{since }e^{mt}\neq0]\\\\\Rightarrow m^2+2\times m\times5+5^2=0\\\\\Rightarrow (m+5)^2=0\\\\\Rightarrow m=-5,-5.](https://tex.z-dn.net/?f=m%5E2e%5E%7Bmt%7D%2B10me%5E%7Bmt%7D%2B25e%5E%7Bmt%7D%3D0%5C%5C%5C%5C%5CRightarrow%20%28m%5E2%2B10y%2B25%29e%5E%7Bmt%7D%3D0%5C%5C%5C%5C%5CRightarrow%20m%5E2%2B10m%2B25%3D0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~%5B%5Ctextup%7Bsince%20%7De%5E%7Bmt%7D%5Cneq0%5D%5C%5C%5C%5C%5CRightarrow%20m%5E2%2B2%5Ctimes%20m%5Ctimes5%2B5%5E2%3D0%5C%5C%5C%5C%5CRightarrow%20%28m%2B5%29%5E2%3D0%5C%5C%5C%5C%5CRightarrow%20m%3D-5%2C-5.)
So, the general solution of the given equation is
Differentiating with respect to t, we get
According to the given conditions, we have
and
Thus, the required solution is
Answer:
The difference of squares is (a - b)(a + b) = a² - b². Since a = x and b = 2, the answer is x² - 4.
Answer:
Step-by-step explanation:
8/3=3(c+5/3)
multiply both sides by 3
8=9(c+5/3)
divide both sides by 9
8/9=c+5/3
subtract 5/3 from both sides
c=8/9-5/3
change 5/3 to 15/9
c=8/9-15/9
c=-7/9
Answer:
$19.24 is the overtime rate $579.67 one week
Step-by-step explanation:
So $13.00 its $19.50 so I subtracted $12.74 to $13.00 got 0.26 then subtracted $19.50 by 0.26 and got $19.24
$12.74 times 45.5 that will be $579.67 for just one week
If I didn't get it right. Tell me in the comments. I think I got it right.
