How do you solve using the quadratic formula 6x+9=2x^2?

2 Answers
Apr 13, 2018

x=3/2+3/2 sqrt 3 or x=3/2-3/2 sqrt 3

Explanation:

6x+9=2x^2

:.2x^2=6x+9

:.2x^2-6x-9=0

Quadratic formula:- x=ax^2+bx+c

:.a=2,b=-6 and c=-9

:.x=(-b+-sqrt (b^2-4ac))/(2a)

:.x=(-(-6)+-sqrt((-6^2)-4(2)(-9)))/(2(2))

:.x=(6+-sqrt(108))/4

:.x=(6+-sqrt(3*3*3*2*2))/4

:.sqrt2*sqrt2=2

:.sqrt 3*sqrt 3=3

:.x=(6+-3*2 sqrt 3)/4

:.x=(6+-6 sqrt 3)/4

:.x=cancel 6^3/cancel 4^2+-(cancel 6^3 sqrt 3)/cancel 4^2

:.x=3/2+-(3 sqrt 3)/2

:.x=3/2+3/2 sqrt 3 or x=3/2-3/2 sqrt 3

Apr 13, 2018

x=3/2+−3/2sqrt(3) or x=3/2+3/2sqrt3

Explanation:

Step 1: Subtract 2x^2 from both sides.
6x+9−color(blue)(2x^2)=2x^2−color(blue)(2x^2)
−2x^2+6x+9=0
Step 2: Use quadratic formula with color(red)(a=-2), color(purple)(b=6), color(green)(c=9).
x=−b±sqrt(b^2−4ac)/(2a)
x=−(color(purple)(6))^2±sqrt((color(purple)(6))^2−4(color(red)(−2))(color(green)(9)))/(2(color(red)(−2))
x=
−6±sqrt108/(−4)
x=3/2+−3/2sqrt3 or x=3/2+3/2 sqrt3