Solve the quadratic equation x² - 12x+32=0
Answers
Step-by-step explanation:
Given:-
the quadratic equation x^2 - 12x+32=0
To find:-
Solve the quadratic equation x^2 - 12x+32=0
Solution:-
Given equation is x^2 - 12x+32=0
Method -1:-
Factorization method:-
Given equation is x^2 - 12x+32=0
=>x^2 - 8x -4x +32 = 0
=>x(x-8)-4(x-8) = 0
=>(x-8)(x-4) = 0
=>x-8 = 0 or x-4 = 0
=>x= 8 and x=4
Solution is 4 and 8
Method-2:-
Completing the square method:-
Given equation is x^2-12x+32 = 0
=>x^2 -12x = -32
=>x^2 -2(6x)=-32
=>x^2-2(x)(6) = -32
on adding 6^2 both sides then
=>x^2 - 2(x)(6) + 6^2 = -32 +6^2
=>(x-6)^2 = -32+36
=>(x-6)^2 = 4
=>(x-6)=±√4
=>x-6 = ±2
=>x=6±2
=>x = 6+2 and 6-2
=>x=8 and 4
Solution is 4 and 8
Method-3:-
Quadratic formula method:-
Sridharacharya formula:-
Given equation is x^2-12x+32 = 0
On comparing with the standard quadratic equation ax^2 +bx +c =0
a= 1
b=-12
c=32
x= [{-b±√(b^2-4ac)}/(2a)]
=>x=[-(-12)±√{(-12)^2-4(1)(32)}\(2×1)]
=>x=[12±√(144-128)/2]
=>x=[12±√16]/2
=>x=(12±4)/2
=>x=2(6±2)/2
=>x=6±2
=>x=6+2 and 6-2
=>x=8 and 4
Solution is 4 and 8
Answer:-
The solution for the given equation is 4 and 8