-6(u+5)^2=120
-5 + or - 4i squareroot 5
-5 to both sides?
so what about the u?
in the parenthises with the five, what happens to that?
Take the (u+5)^2 and solve (u+5)(u+5)
that gives you -6(u^2-10u-25)=120
then distribute the -6
-6u^2-60u-150= 120 then subtract 120 from both sides
-6u^2-60u-270=0 then divide everythin by -6 giving you
u^2+10u+45=0 then use the quadratic formula
(-b +/- squareroot b^2 -4ac)/2a
then you will get the answer. If you don't know how to use the quadratic formula then let me know.
To solve the equation -6(u+5)^2 = 120, we can follow these steps:
Step 1: Simplify the equation
Expand the square by multiplying (u+5) by itself:
-6(u+5)(u+5) = 120
Using the distributive property, multiply -6 by each term inside the parentheses:
-6(u^2 + 10u + 25) = 120
Multiply -6 by each term:
-6u^2 - 60u - 150 = 120
Step 2: Move the constants to one side
Rearrange the equation by adding 120 to both sides:
-6u^2 - 60u - 150 + 120 = 120 + 120
This simplifies to:
-6u^2 - 60u - 30 = 0
Step 3: Divide by the common factor
Divide the entire equation by -6 to simplify:
(-6u^2 - 60u - 30) / -6 = 0 / -6
This gives us:
u^2 + 10u + 5 = 0
Step 4: Solve the quadratic equation
To solve the quadratic equation u^2 + 10u + 5 = 0, we can use factoring, completing the square, or the quadratic formula. In this case, factoring may not be straightforward, so let's use the quadratic formula:
The quadratic formula is:
u = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = 1, b = 10, and c = 5:
u = (-10 ± √(10^2 - 4(1)(5))) / (2*1)
Simplifying further:
u = (-10 ± √(100 - 20)) / 2
u = (-10 ± √80) / 2
u = (-10 ± 4√5) / 2
Step 5: Simplify the solution
We can simplify the expression by dividing the numerator and denominator by 2:
u = -5 ± 2√5
Therefore, the solutions to the equation -6(u+5)^2 = 120 are:
u = -5 + 2√5
u = -5 - 2√5