Question

Solve by factoring write the steps.

x2−7x+10=0
Please help show me all the steps and the answers

Answer 1

x^2−7x+10=0

Step 1: Factor left side of equation.
(x−2)(x−5)=0
Step 2: Set factors equal to 0.
x−2=0 or x−5=0
x=2 or x=5
Answer: x=2 or x=5

Answer 2

`x^(2) - 7x +10 = 0`

The middle term should be factored in such a way that the sum of two numbers is -7x and their product is 10x2. These two factors are -5x and -2x. So re-writing the equation, we get:


`x^(2) - 5x - 2x +10 = 0`

Taking common, we get:


`x( x - 5) -2 (x-5)=0 \\ \\ (x-5)(x-2)=0`

This means:
x - 5 = 0
⇒ x = 5

or

x - 2 = 0
⇒ x = 2

Therefore, the solution to the given equation are x = 2 and x = 5