Question

Which is a solution to the equation?

(x - 3)(x - 5) = 35
x= -8
x=-5
x=2
x = 10

Answer 1

Answer: x = 10


Just plug in the different numbers to see which ones equal 35.

I’m going to plug in x = -8 into the equation
(x - 3)(x - 5) = 35
(-8 - 3)(-8 - 5) = 35 (substitute -8 for x)
(-11)(-13) = 35
143 = 35
This answer is wrong because 143 does not equal 35

Now let’s plug in x = 10
(x - 3)(x - 5) = 35
(10 - 3)(10 - 5) = 35 (substitute 10 for x)
(7)(5) = 35
35 = 35
This solution works because 35 equals 35

Answer 2

(x-3)(x-5)=35

Multiply the brackets together

x*x-5*x-3*x-3*5

x^2-8x+15=35

Move +35 to the other side. Sign changes from +35 to -35

x^2-8x+15-35=35-35

x^2-8x-20=0

(x-10)(x+2)=0

x-10=0 x+2=0

Move -10 to the other side. Sign changes from -10 to +10

x-10+10=0+10 x+2-2=0-2

x=10 x=-2

Answer: x=10