Question

How do you solve `x^2+9=10x`?

Answer 1

1 and 9

Explanation:

`y = x^2 - 10x + 9 = 0.`
Find 2 real roots, knowing sum (-b = 10) and product (c = 9).
They are 1 and 9.

Answer 2

`9,1`

Explanation:

`color(blue)(x^2+9=10x`

Subtract `10x` both sides

`rarrx^2+9-10x=cancel(10x-10x`

`rarrx^2+9-10x=0`

Rewrite the equation in Standard form (`ax^2+bx+c=0`)

`color(purple)(rarrx^2-10x+9=0`

This is a Quadratic formula

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

Remember that `aand b` are the coefficients and `c` is the constant

So,

`color(violet)(a=1`

`color(violet)(b=-10`

`color(violet)(c=9`

`rarrx=(-(-10)+-sqrt(-10^2-4(1)(9)))/(2(1))`

`rarrx=(10+-sqrt(100-(36)))/(2)`

`rarrx=(10+-sqrt(64))/(2)`

`rarrx=(10+-8)/(2)`

`rarrx=(cancel10^5+-cancel8^4)/(cancel2^1)`

`rarrx=5+-4`

Remember that `+-` means "plus or minus",

Which implies that,

`color(indigo)(x=5+4=9`

`color(orange)(x=5-4=1`

`color(blue)( ul bar |x=9,1|`

If you are confused with the Quadratic formula

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