Question

One of the two solutions to the equation $5x^2 - 11x - 36 = 0$ is $x = 4$. What is the other solution?

Answer 1

Following are the calculation to the given equation:

Given:

$\to 5x^2 - 11x - 36 = 0$

one solution:

$x=4$

To find:

other solution=?

Solution:

$\to 5x^2 - 11x - 36 = 0\\\\\to 5x^2 - (20-9)x - 36 = 0\\\\\to 5x^2 - 20x+9x - 36 = 0\\\\\to 5x(x - 4)+9(x - 4) = 0\\\\\to (x - 4) (5x+9) = 0\\\\\to x - 4=0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 5x+9 = 0\\\\\to x = 4 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 5x = -9\\\\\to x = 4 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = \frac{-9}{5}$

Therefore, another solution is "$-\frac{9}{5}$".

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Answer 2

the other solution is$\frac{-9}{5}$

Answer:

Solution given:

$5x^2 -11x-36=0$

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

$5x^2 -(20-9)x-36=0$open bracket

$5x^2 -20x+9x-36=0$

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=$\frac{-9}{5}$

Step-by-step explanation: