how to solve this

Question

Solve the quadratic equation

x² - 8 x + 15 = 0

Answer 1

x^2 - 8x+15=0

(x-3)(x-5) = 0

x = 3, 5

if you didn't figure out the factors

complete the square. Add the square of half the linear term's coefficient, (-8/2)^2= 4^2 = 16

x^2 - 8x +16 = -15 +16 = 1

(x-4)^2 = 1

x-4 = +/-1

x = 4+/-1 = 3, 5

or use the quadratic formula:

x=-b/2a +/-(1/2a)sqr(b^2-4ac)

where a=1,b=-8, c=15

x = 8/2 +/-.5sqr(64-60)

= 4 +/-.5sqr4

= 4+/-1

= 3, 5

check the answers

plug them into the original equation

f(3) =x^2-8x +15

= 3^2 -8(3)+15

= 9-24+15

=0

f(5)=5^2 -8(5)+15

=25 -40+15

= 0

or just graph the parabola and find the x intercepts = the real solutions