Question

How do you solve `6x ^ { 2} - 24x - 270= 0`?

Answer 1

See a solution process below:

Explanation:

First, divide each side of the equation by `color(red)(3)` to reduce the coefficients while keeping the equation balanced:

`(6x^2 - 24x - 270)/color(red)(3) = 0/color(red)(3)`

`(6x^2)/color(red)(3) - (24x)/color(red)(3) - 270/color(red)(3) = 0`

`2x^2 - 8x - 90 = 0`

Now, we can use the quadratic formula to solve the problem.

The quadratic formula states:

For `ax^2 + bx + c = 0`, the values of `x` which are the solutions to the equation are given by:

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

Substituting `2` for `a`; `-8` for `b` and `-90` for `c` gives:

`x = (-(-8) +- sqrt((-8)^2 - (4 * 2 * -90)))/(2 * 2)`

`x = (8 +- sqrt(64 - (-720)))/4`

`x = (8 +- sqrt(64 + 720))/4`

`x = (8)/4 +- sqrt(784)/4`

`x = 2 +- 28/4`

`x = 2 + 7` and `x = 2 - 7`

`x = 9` and `x = -5`

Answer 2

-5 and 9

Explanation:

`y = 6(x^2 - 4x - 45) = 0.`
Solve the quadratic equation in the parentheses. Find 2 numbers knowing the sum (-b = 4) and the product (c = - 45):
They are: -5 and 9.