(x+5)(x-3)=9 I am not sure how to work this out?
mutiply out the 2 factors and subrtract 91 from both side to equate equation to zero then solve for root
x^2+5x-3x-15=9
x^2+2x=9+15
x^2+2x=24
x^2+2x+1=24+1
(x+1)^2=25
Becouse: (x+1)^2=x^2+2x+1
x+1=sqroot(25)
x+1=5 and
x+1=-5
x+1=5
x=5-1=4
x+1=-5
x=-5-1=-6
Solutions is:
x=4 and x=-6
To solve the equation (x+5)(x-3) = 9, you can follow these steps:
Step 1: Expand the equation using the distributive property:
(x+5)(x-3) = 9
(x+5)x + (x+5)(-3) = 9
x^2 + 5x - 3x - 15 = 9
Step 2: Simplify the equation by combining like terms:
x^2 + 2x - 15 = 9
Step 3: Rearrange the equation to bring everything to one side:
x^2 + 2x - 15 - 9 = 0
x^2 + 2x - 24 = 0
Step 4: Factor the quadratic equation, if possible:
To factor the equation, we need to find two numbers whose sum is 2 and whose product is -24. After some trial and error, we find that the numbers are +6 and -4:
(x + 6)(x - 4) = 0
Step 5: Apply the zero product property:
If the product of two factors is zero, then at least one of the factors must be zero. So, we solve for x in each factor:
x + 6 = 0 or x - 4 = 0
Step 6: Solve for x:
For the first factor:
x + 6 = 0
x = -6
For the second factor:
x - 4 = 0
x = 4
Therefore, the solutions to the equation (x+5)(x-3) = 9 are x = -6 and x = 4.