x2 + 5x – 9 = 5 Which of the following values of x satisfies the equation. Please step by step solving so I may understand.

Question

7

3

–2

–7

Answer 1

The equation is X² + 5X - 9 = 5.

This can be solved using the choice X = -7 (the 4th choice in the list).

(-7)² + 5(-7) - 9 = 5.

Subtract 5 from both sides to get

49 -35 - 9 - 5 = 49 - 49 = 0.

Amy I's method is correct in how you can find 2 possible answers to a quadratic equation, but only one of them was given as an option and that was -7.

Answer 2

Hello Maria,

Since this is a quadratic equation we know that there will be TWO roots(zeros, solutions).

First get the equation = 0 by subtracting 5 from BOTH sides

x ² + 5 x - 9 = 5 Normally, we need to get the equation = 0 on one side

-5 = - 5

x ² + 5 x - 14 = 0 simplified

NOW since it is a quadratic equation the most common methods to solve are by factoring or using the QUADRATIC FORMULA.

Because the x² coefficient is a 1 we can just REVERSE the FOIL {First, Outside, Inside, Last}

Since the last term, the constant,is a negative then one factor will be ( x + ? ) and the other factor will be (x - ??) .

we need to find two numbers that we can MULTIPLY to get (- 14 ) but add them and get (+5). We are undoing the FOIL. Sometimes we just have to try different combinations until we find the right one.

( x + 7 ) ( x - 2) = x ² - 2 x + 7 x -14 = x ² + 5x - 14 = 0 so the solutions are - 7 and 2. BOTH of them check the ORIGINAL equation. So I think maybe there is a typo in your list of answers.

I hope this was enough detail for you. Also, you could have just taken each one of the "answers" and substituted them one at a time into the original equation to see which work. That won't work though if it isn't multiple choice .

Answer 3

Hi Maria,

Here is another quick answer to your question :

1. Here is your equation : X² + 5X - 9 = 5
2. To solve this equation the right side of it should be equal to zero and to make this we should transfer the value "5" to the other side with a "-" value.
3. New equation : X² + 5X - 9 -5 = 0 -----> X² + 5X - 14 = 0
4. If an equation includes a "X^2" and also "X" inside it, that means there are two X values that will solve it, X_{1 =} a and X_{2 =} b,
5. Another form of this equation is (X + a) (X+b) = 0
6. To find a and b values, we have some clues :
7. Their multiplication should be -14 -----> X² + 5X - 14 = 0
8. Their total sum should be 5 -----> X² + 5X - 14 = 0
9. Lets figure out these values : (-2) X (7) = 14 and (-2) + (7) = 5 ---> (X -2) (X+7) = X² + 7X -2X - 14 ----> X² + 5X - 14 = 0
10. We found the values
11. First value = (X-2) = 0 --> X =2
12. Second value = (X+7) = 0 --> X =-7

Result is : 2, -7

Lets crosscheck the results :

First value = 2 ----> X² + 5X - 14 = 0 ---> 2² +5*2 -14 = 4 +10 -14 = 0

Second value = -7----> X² + 5X - 14 = 0 ---> (-7)² +5*(-7) -14 = 49 -35-14 = 0

I hope that helps you understand the way of solution.

Sincerely,

Answer 4

7x-9=5

7x=14

x=2

Not up there.