Question

Hello people ~
factorise: 21x² - 55x - 14​

Answer 1

`\displaystyle [7x - 2][3x - 7]`

Explanation:

Find two quantities that when summed to 55, they also multiply to 294. Those will be 6 and 49. The TINIER quantity gets the plus sign because the B-value is −55, therefore 49 gets the minus sign, leaving 6 with the plus sign. In extension, sinse we have a leading coefficient greater than one, we need to take extra procedures. Here is how it is done:

I am joyous to assist you at any time.

**For all you moderatours out there, this user made a typographical errour with the symbol of the C-value. It was supposed to be 14, not −14. BELIEVE ME.

Answer 2

This equation cannot be factorised, at least not easily. It would require decimals and that's not worth the time. Instead you can use the quadratic formula to solve for x, which works for any quadratic equation:

`\frac{-b + or - \sqrt{b^(2) - 4ac} }{2a}`

a being the x^2 coefficient

b the x coefficient

and c the constant

here a = 21

b = -55

c = -14

let's solve this one:

`\frac{-(-55) + \sqrt{(-55)^(2) - 4(21)(-14)} }{2(21)}`

You can simply input this into a calculator to find the answer, or you can work it out mentally.

= 2.852740993

Now, since this is a quadratic we need to possible values of x. So we just redo the same formula, but this time with a negative square root:

`\frac{-(-55) - \sqrt{(-55)^(2) - 4(21)(-14)} }{2(21)}`

= -0.2336933736

You can round these answers however you like, but I would recommend doing to either 3 significant figures, either 2 or 3 decimal places.