Question

Solve the following:
a. 4x^2 + 5x + 3 = 2x^2 − 3x
b. c^2 − 14 = 5c

Answer 1

(a) x = -0.418 , -3.581

(B) c = 6.855, -1.855

Explanation:

(A) We have given equation
`4x^2+5x+3=2x^2-3x`

`2x^2+8x+3=0`

On comparing with standard quadratic equation
`ax^2+bx+c`

a = 2, b = 8 and c = 3

So roots of the equation will be
`x=(-b\pm √(b^2-4ac))/(2a)=(-8\pm √(8^2-4* 2* 3))/(2* 2)=(-8\pm 6.324)/(4)=-0.418,-3.581`

(b)
`c^2-14=5c`

`c^2-5c-14=0`

a = 1, b = -5 and c= -14

So
`c=(-b\pm √(b^2-4ac))/(2a)=(-(-5)\pm √((-5)^2-4* 1* (-14)))/(2* 1)=(5\pm 8.71)/(2)=6.855,-1.855`