Solve the equation: x²-10x+21=0?

(x - 7)(x - 3) = 0
x = 7 , x = 3

Factor the equation to

(x - 7)(x - 3) = 0

So the answer is

x=7, x=3

Solve by factoring:

x^2 + -10x + 21 = 0
(x + -3)(x + -7)
x + -3 = 0
x + -7 = 0
x = 3, 7

Solve by completing the square:

x^2 + -10x + 21 = 0
x^2 + -10x + 21 + 4 = 4
x^2 + -10x + 25 = 4
(x + -5)^2 = 4
x = sqrt(4) + 5, -sqrt(4) + 5
x = 7, 3

Solve by quadratic formula:

-b + sqrt(b^2 + -4ac) / 2a
-b + -sqrt(b^2 + -4ac) / 2a

10 + sqrt(-10^2 + (-4*1*21)) / 2*1
= 7
10 + -sqrt(-10^2 + (-4*1*21)) / 2*1
= 3

(x-7)(x-3)

x² - 10x + 21 = 0
x² - 3x - 7x + 21 = 0
x(x - 3) - 7(x - 3) = 0
(x - 7)(x - 3) = 0

x = 7 or x = 3

x^2 - 10x + 21 = 0
(x - 3)(x - 7) = 0

x - 3 = 0
x = 3

x - 7 = 0
x = 7

∴ x = 3 or 7

x²-10x+21=0
x²+(-3-7)x+21=0
x²-3x-7x+21=0
Taking x common from x²-3x and 7 common from 7x+21
x(x-3)-7(x-3)=0
Taking (x-3) common
(x-3){x-7}=0
either x-3=0, x=3
or x-7=0 , x=7
x= {3,7}

x²-10x+21=0

factor:

(x - 7)(x - 3) = 0

set each equal to 0:

x - 7 = 0
x = 7

and

x - 3 = 0
x = 3

Therefore x = 7, 3