the other solution is[tex]\frac{-9}{5}[/tex]
Answer:
Solution given:
[tex]5x^2 -11x-36=0[/tex]
doing middle term factorization
we need to get 11 by subtracting product of 5 and 36.
5*36=180=2*2*3*3*5
we get 11 by subtracting 5*2*2-3*3=20-9
substituting value of 11 as (20-9)
now
[tex]5x^2 -(20-9)x-36=0[/tex]open bracket
[tex]5x^2 -20x+9x-36=0[/tex]
taking common from each two terms
5x(x-4)+9(x-4)=0
again taking common
(x-4)(5x+9)=0
either
x-4=0
x=4
or
5x+9=0
5x=-9
x=[tex]\frac{-9}{5}[/tex]
Step-by-step explanation:
Following are the calculation to the given equation:
Given:
[tex]\to 5x^2 - 11x - 36 = 0[/tex]
one solution:
[tex]x=4[/tex]
To find:
other solution=?
Solution:
[tex]\to 5x^2 - 11x - 36 = 0\\\\\to 5x^2 - (20-9)x - 36 = 0\\\\\to 5x^2 - 20x+9x - 36 = 0\\\\\to 5x(x - 4)+9(x - 4) = 0\\\\\to (x - 4) (5x+9) = 0\\\\\to x - 4=0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 5x+9 = 0\\\\\to x = 4 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 5x = -9\\\\\to x = 4 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = \frac{-9}{5}\\[/tex]
Therefore, another solution is "[tex]-\frac{9}{5}[/tex]".
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