To find the equation that has exactly the same solutions as (x - 7) (x + 9) = 0, we can use the Zero Product Property, which states that if a * b = 0, then either a = 0 or b = 0.
Given the equation (x - 7) (x + 9) = 0, we can set each factor equal to 0 and solve for x:
x - 7 = 0 or x + 9 = 0
Solving for x in each equation:
x - 7 = 0
x = 7
x + 9 = 0
x = -9
The solutions to the given equation are x = 7 and x = -9.
Now let's check which of the equations A, B, C, and D have the same solutions.
A. x^2 + 2x = -63
Rearranging this equation:
x^2 + 2x + 63 = 0
This equation is different from the original equation, so it does not have the same solutions.
B. x^2 - 2x - 63 = 0
This equation is the same as the original equation, so it has the same solutions.
C. x^2 = -2x + 63
Rearranging this equation:
x^2 + 2x - 63 = 0
This equation is different from the original equation, so it does not have the same solutions.
D. x^2 = 2x - 63
Rearranging this equation:
x^2 - 2x + 63 = 0
This equation is different from the original equation, so it does not have the same solutions.
Therefore, the equation that has exactly the same solutions as (x - 7) (x + 9) = 0 is B. x^2 - 2x - 63 = 0.
Which of the following equations has exactly the same solutions as (x - 7) (x + 9) = 0?
A. x^2 + 2x = -63
B. x^2 - 2x - 63 = 0
C. x^2 = -2x + 63
D. x^2 = 2x - 63
1 answer