SOLUTION: Why cant you solve x(x + 5) = 24 by solving x = 24 and x + 5 = 24? What makes this not possible? Thanks.

Question 1030563: Why cant you solve x(x + 5) = 24 by solving x = 24 and x + 5 = 24?
What makes this not possible? Thanks.
Found 2 solutions by josgarithmetic, Theo:
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
The two last statements are wrong. You are trying to relate two factors, unknown ones, to 24. What happens if you try to evaluate x+5=25 using x=24?

Very clearly false.

The goal would be solve for the variable, x.
, and you may expect two integers to give the product 24.
-

Is this factorable? If yes, THEN YOU COULD USE ZERO PRODUCT RULE.

-
Obviously the two possible solutions for x are 3 or -8.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
your equation is x * (x + 5) = 24

you first need to simplify the equation by applying the distributive law of multiplication to get:

x^2 + 5x = 24

you then need to subtract 24 from both sides of the equation to get:

x^2 + 5x - 24 = 0

you then need to factor this equation to get:

(x + 8) * (x - 3) = 0

now that you have the factors equal to 0, you can solve for:

x + 8 = 0 which results in x = -8

x - 3 = 0 which results in x = 3.

why can you do this?

because 0 * (x-3) = 0 and (x + 8) * 0 = 0

your original equation was x * (x-5) = 24

you can't solve it the way you solved the factored quadratic equation because the result is not 0.

x * (x+5) = 24 won't work.

if it was x * (x+5) = 0, then it would work.

but it's not.

you could subtract 24 from both sides of the equation to get:

x * (x+5) - 24 = 0

but you still have to simplify it by using the distributive law of multiplication to get:

x^2 + 5x - 24 = 0 and then factor that to get (x+8) * (x-3) = 0.

only then can you separate out the factors and set them equal to 0 and then solve.

let's assume you could do x * (x+5) = 24 and split it up like:

x = 24
x + 5 = 24

you would get x = 24 or x = 19

you would then need to confirm if these solutions were correct by replacing x in the original equations.

when x = 24, x * (x+5) = 24 becomes 24 * 29 = 24 which is clearly not true.

when x = 19, x * (x+5) = 24 becomes 19 * 24 = 24 which is clearly not true again.

solving it the right way, you get x = -8 or x = 3

when x = -8, x * (x+5) = 24 becomes -8 * ( -8 + 5) = 24 which becomes -8 * -3 = 24 which becomes 24 = 24 which is true.

when x = 3, x * (x+5) = 24 becomes 3 * (3 + 5) = 3 * 8 = 24 which becomes 24 = 24 which is also true.

breaking up the factors into two separate equations only works when the result is equal to 0.

x * (x+5) = 0 would work, but x * (x+5) = 24 will not.

you needed to convert the equation into its quadratic equivalent and then you need to set that equation equal to 0 and then you needed to factor it to get your answer.

x * (x+5) = 24 becomes x * (x+5) - 24 = 0 which becomes x^2 + 5x - 24 = 0 which is then factored to be (x+8) * (x-3) = 0.

only then could you set x+8 = 0 and x-3 = 0 to solve for x.

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