Please use factoring: 12x^2 + 25 = 40x?

12x^2 + 25 = 40x
or, 12x^2 -40x + 25 = 0
or, 12x^2 -30x- 10x + 25 = 0
or, 6x(2x - 5) - 5(2x - 5) = 0
or, (2x - 5)(6x - 5) = 0
=>2x - 5 = 0 or 6x - 5 = 0
=>2x = 5 or 6x = 5
=> x = 5/2 or x = 5/6 Ans.

ok, enable's initiate with the coefficients with optimal and lowest order, sixteen and 25. The sq. root of sixteen is 4 and the sq. root of 25 is 5. So we initiate with something like this: (4x _ 5)(4x _ 5) now we would desire to seek for an indication which will artwork. because of the fact the 1st sign is beneficial (the sixteen is beneficial) and the final one is beneficial too (the 25 is beneficial) however the single in the middle is unfavourable (the 40 is unfavourable) there must be some unfavourable in the factorization. the only thank you to get a favorable in the final one is to have the two (4x + 5)(4x + 5) or (4x - 5)(4x - 5), in case you utilize the single with 2 positives you will no longer get a unfavourable. So the terrific suited factorization is (4x - 5)(4x - 5). you may verify it by way of multiplying. (4x - 5)(4x - 5) = 16x^2 - 20x - 20x +25 = 16x^2 -40x +25 (it fairly is terrific suited!) (4x - 5)(4x - 5) may be written as (4x - 5)^2. and that's the factorization. i desire i might desire to help :)

Using the formula

-b(+/-)sqrt(b^2-4ac)/2a..................1

the equation can be written as:

12x^2-40x+25=0....................2

Standard equation:

ax^2+bx+c=0....................3

Equating both the equations:

a=12, b=-40, c=25

put the above value in the equation 1

40(+/-)sqrt[(-40)*(-40)-4(12)(25)]/2*12

40(+/-)sqrt[1600-1200]/24

40(+/-)sqrt[400]/24

40(+/-)20/24

First answer --------2.5 if +ve

Second answer--------------.833 -ve

12x^2 + 25 = 40x
12x^2 - 40x + 25 = 0
12x^2 - 10x - 30x + 25 =0
(12x^2 - 10x) - (30x - 25) = 0
2x(6x - 5) - 5(6x - 5) = 0
(6x - 5)(2x - 5) = 0

6x - 5 = 0
6x = 5
x = 5/6

2x - 5 = 0
2x = 5
x = 5/2 (2.5)

∴ x = 5/6, 5/2 (2.5)

12x² + 25 = 40x
12x² + 25 – 40x = 0
(2x – 5)(6x – 5) = 0
(2x – 5) = 0
2x = 5
x = 5/2
(6x – 5) = 0
6x = 5
x = 5/6

x = (5/2, 5/6}

12 x ² - 40 x + 25 = 0

( 6x - 5 ) ( 2x - 5 ) = 0

x = 5/6 , x = 5/2

12x^2 + 25 = 40x
12x^2 - 40x + 25 = 0
(2x - 5)(6x - 5) = 0
2x - 5 = 0 and 6x - 5 = 0
2x = 5 and 6x = 5
x = 5/2 and x = 5/6