Solve the quadratic equation 25x2-30x=-9 by factoring?

Question

The problem is 25x(squared) - 30x = -9

The choices for the answer are:

x= 3/5
x= 5/3
x= -5/3
x= -3/5

Answer 1

x= 3/5

If you factor by grouping you would get
25x^2 - 15x -15x + 9 = 0

then you would factor the first two terms and the last two terms
5x(5x-3) -3(5x-3) = 0

use the terms outside the parentheses are one factor and the one inside the parentheses as the second factor
(5x-3)(5x-3) = 0

set to zero
5x-3 = 0

do algebra
x=3/5

or you could have just noticed that that equation is a perfect square

Answer 2

Ok this is a classic case of (A + B)^2 = A^2 + 2AB + B^2.

In this case A = 5x because sqrt(25x^2) = 5x or -5x and B is -3 because sqrt(9) = 3 or -3. 2*5x*-3 also equals -30. In fact if you want to be weird it is also (-5x + 3)^2 but we normally write it so that the first term is positive.

Anyway (5x -3)^2 = 0, so (5x - 3) = 0, so 5x = 3, so x = 3/5.

Answer 3

25x^2 - 30x + 9 = 0
(5x - 3)^2 = 0
5x - 3 = 0
5x = 3
x = 3/5

Answer 4

set it equal to zero, so 25x2-30x+9=0. Then you find something that multiplies to the the product of the first and last coefficients, and adds to the middle one. So something that multiplies to 225 and adds to -30.

This would be -25 and -5

You can factor it using these two numbers to help you out.

Answer 5

25x2-30x=-9
25x^2-30x+9=0
(5x-3)^2=0
5x-3=0
x=3/5

Answer 6

(5x-3)^2
x= 3/5