6x^2-10x-16=0?

3 Answers
Jun 15, 2018

Solve the quadratic to get x=-1, 8/3

Explanation:

I assume the question wants the solutions for x.

Divide through to make the first coefficient 1:
x^2-5/3x-8/3=0

Complete the square:
(x-5/6)^2-25/36-8/3=0
(x-5/6)^2=121/36

x=5/6+-sqrt(121/36)=5/6+-11/6

So x=-1, 8/3.

Jun 16, 2018

y = 6x^2 - 10x - 16 = 0
Since a - b + c = 0, use shortcut.
The 2 real roots are:
x = -1 ,and x = -c/a = 16/6 = 8/3

Reminder of shortcut .
If a + b + c = 0, the 2 real roots are: x = 1, and x = c/a
Example 1. Solve: 3x^2 + 7x - 10 = 0
x = 1, and x = c/a = -10/3
If a - b + c = 0, the 2 real roots are: x = -1, and x = -c/a
Example 2. Solve: 4x^2 - 5x - 9 = 0
x = -1, and x = -c/a = 9/4

Jun 16, 2018

Another way

Explanation:

if ax^2+bx+c=0

x = (-bpmsqrt(b^2-4ac))/(2a)

In this case a = 6,b=-10, c = -16

x = ( -(-10) pm sqrt( (-10)^2 - ( 4 * 6 * (-16 ) ) ) )/(2*6)

x = (10pmsqrt(484) )/12

x = (10 pm22 )/12

x = {8/3 , -1 }