Which of the following equations has only one solution?
x(x - 1) = 9
x2 - 6x + 9 = 0
x²=9

x2 - 6x + 9 = 0

Step-by-step explanation:

Factorize the equation: take 9 and split it into its factors 3 and 3.

After factorization, determine the signs by looking at the middle term. Since it's negative, the greater factor will be negative while the other will be positive. However, here it doesn't make a difference because both numbers are 3.

We're left with this

(x-3) (x-3) = 0

x-3=0 and x-3=0

By adding 3 to both sides in the first equation, we find out that x=3

The same also happens with the second equation, so x=3 as well.

Since both answers are the same, they are one solution.

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.