Question

How do you solve `8x-10=x^2-7x+3` using the quadratic formula?

Answer 1

Convert the given equation into standard quadratic form and then apply the quadratic formula to get
`color(white)("XXX")x=(15+-sqrt(173))/2`

Explanation:

The standard quadratic form is
`color(white)("XXX")color(red)ax^2+color(blue)bx+color(green)c=0`
with solutions given by the quadratic formula
`color(white)("XXX")x=(-color(blue)b+-sqrt(color(blue)b^2-4color(red)acolor(green)c))/(2color(red)a)`

Converting the given equation:
`color(white)("XXX")8x-10=x^2-7x+3`
into standard form results in
`color(white)("XXX")color(red)1x^2+color(blue)(""(-15))x+color(green)(13)=0`

Plugging the coefficient values into the quadratic formula gives the result shown in the answer above.

Answer 2

Answers(to 3 d.p.): 0.924 and 14.077

Explanation:

Since you have

`8x - 10 =` `x^2 - 7x+3`,

You transfer the numbers on the left hand side to the right in order to get the normal order: `ax^2 ± bx ± c`.

`8x - 10 =` `x^2 - 7x +3`

If you add 10 on both sides, you eliminate the -10 on the left and bring it to the right.

`8x - 10 +10 =` `x^2 - 7x +3 + 10`

= `8x =` `x^2 - 7x +13`

Do the same for the 8x until you get 0.

`8x -8x =` `x^2 - 7x +13-8x`

= `0 =` `x^2 - 15x +13`

= `x^2 - 15x +13`

So now that you have everything in order, you can input the coefficients into the quadratic formula:

`x=(-(-15) ± sqrt(225 - 52))/(2×1)`

`=(15 ± sqrt(173))/(2×1)`

`=(15 ± sqrt(173))/2`

`=(15 + sqrt(173))/2`

`=14.077`

`=(15 - sqrt(173))/2`

`=0.924`

Hope this helps!