How do you find the solution to the quadratic equation x^2 - 4x -3 = 0x2−4x−3=0?
3 Answers
Explanation:
"there are no whole numbers which multiply to - 3"there are no whole numbers which multiply to - 3
"and sum to - 4"and sum to - 4
"we can solve using the method of "color(blue)"completing the square"we can solve using the method of completing the square
"the coefficient of the "x^2" term is 1"the coefficient of the x2 term is 1
• " add subtract "(1/2"coefficient of the x-term")^2" to"∙ add subtract (12coefficient of the x-term)2 to
x^2-4xx2−4x
rArrx^2+2(-2)xcolor(red)(+4)color(red)(-4)-3=0⇒x2+2(−2)x+4−4−3=0
rArr(x-2)^2-7=0⇒(x−2)2−7=0
rArr(x-2)^2=7⇒(x−2)2=7
color(blue)"take the square root of both sides"take the square root of both sides
rArrx-2=+-sqrt7larrcolor(blue)"note plus or minus"⇒x−2=±√7←note plus or minus
rArrx=2+-sqrt7larrcolor(red)"exact solutions"⇒x=2±√7←exact solutions
x =
Explanation:
Apply quadratic formula for this equation instead of trying to factor it out.
1/
2/
3/
4/
5/ x =
Explanation:
Here,
OR
Comparing with quadratic equation,
So,