What is the x-intercept of negative 3x squared plus 24x minus 19?

Answer 1

The idea is to solve the equation -3x2 + 24x - 19 = 0. You can use the quadratic formula for this, using a = -3, b = 24, c = 19.

Or complete the square since dividing by -3 will give us 8x, an even coefficient.

-3x2 + 24x - 19 = 0 (add and subtract 48 to the left side)

-3x2 + 24x -48 + 29 = 0 (subtract 29 to both sides, and factor out -3)

-3(x2 - 8x + 16) = -29 (divide by -3 to both sides)

(x - 4)2 = 29/3

x - 4 = ± √(29/3) (add 4 to both sides)

x = 4 ± √(29/3) (multiply by 3/3 inside the radical, if you want to rationalize the denominator)

x = 4 ± (√87)/3