how do u solve 5x^2-15x-9=2 bycomplelting the square?

Answer 1

5x²-15x-9=2
Add 9 and multiply by 1/5:
x²-3x=11/5
Find 1/2 the coefficient of x, square it, and add the result:
x²-3x+9/4=89/20
It's helfpul to understand why we just did that. The reason is that (x+c)²=x²+2cx+c². We're trying to get the equation into a form where it is an exact square of the quantity x+c. We already have the x², and since the coefficient of the x term is -3, this means that 2c=-, so c=-3/2. Squaring this gives us the c² term, which can be added to turn the left side of the equation into a perfect square. That means that we can now do this:
(x-3/2)²=89/20
Now we just take the square root of both sides. Note that there are TWO square roots of every number. If it were up to me, the presence of a radical would automatically indicate both of them, but since I don't control mathematical conventions, we have to indicate this explicitly. So we get:
x-3/2=±√(89/20)
Adding 3/2 to both sides gives us:
x=3/2±√(89/20)
We are technically done at this point, but we can simplify slightly:
x=(3±√(89/5))/2
Or if we wish a numerical solution:
x≈3.6095 or x≈-0.6095

Answer 2

x^2 + 15x = fifty 4 Take the fifty 4 over to the different part to get: x^2 + 15x - fifty 4 = 0 Then discover 2 numbers that multiply jointly to get -fifty 4, and upload jointly to get 15. (18 and -3) Then positioned those numbers into brackets, to get: (x+18) (x-3) = 0 x + 18 = 0 x = -18 or x - 3 = 0 x = 3 in case you multiply those out, it truly is going to go away you with the reply of x^2 + 15x - fifty 4 = 0, it truly is an similar as x^2 + 15x = fifty 4 i'm hoping this enables you!

Answer 3

5x² - 15x - 9 = 2

Transpose -9
5x² - 15x = 11

Divide by 5
x² - 3x = 11/5

Add 9/4 to both sides
x² - 3x + 9/4 = 11/5 + 9/4

Factor the left side, simplify the right side
(x - 3/2)² = 89/20

get sqrt of both sides
x - 3/2 = sqrt89/2sqrt5

Rationalize the right side by multiplying sqrt5/sqrt5
x - 3/2 = sqrt445/10

transpose -3/2 (or -15/10)
x = (-15 ± sqrt445)/10

^_^

Answer 4

Well, 5x^2-15x-11=0
so x^2-3x-11/2=0
so (x+a)(x+b)=0
so x^2+ax+bx+ab=0
so a+b=-15 and ab=-11/2
it won't work. a and b are irrational. Use the general solution for quadratics to solve.

Answer 5

change the equation to complete square form first.

5x^2-15x-11=0
(divide by 5)
x^2-3x-11/5=0
(move 11/5 to the right)
x^2-3x=11/5
(add (-3/2)^2 to both sides)
x^2-3x+(-3/2)^2=11/5+(-3/2)^2
(express the left side to complete square form)
(x-3/2)^2=11/5+(-3/2)^2
(square root both sides)
x-3/2=+_sqrt[11/5+(-3/2)^2]
(move -3/2 to the right side)
x=+_2.109 +3/2
therefore,
x=3.609,x=-0.609

Answer 6

Just factor it....pretty damned simple.

Answer 7

i have no idea wutsoever..lol