Step by step
The question
Question: find the value of −x² + 5x when x = −1.
−x2 + 5x
x = −1
1 Put the numbers in
We put −1 in place of x.
5x means 5 times x.
So we write a times sign.
A negative number goes in brackets, so its minus stays with it.
= −(−1)2 + 5 × (−1)
5x = 5 × x
2 Powers
Powers come before plus and times.
In −(−1)², the power is only on the −1.
The minus stays in front.
Order: ( ) → x² √ → × ÷ → + −
Careful!
It is not (−−1)1)².
Without brackets, the minus stays outside.
Careful: not −(−1)2 = 1 ✗
(−1)² means −1 times −1.
Minus times minus is plus.
(−1)2 = (−1) × (−1) = 1
That is 1.
= −1 + 5 × (−1)
3 Times and divide
Times comes before plus.
+ × − = −
Plus times minus is minus.
5 times 1 is 5.
So we get −5.
= −1 + (−5)
4 Plus and minus
Adding a negative is the same as taking away.
+ (−) = −
So −1 + (−5) becomes −1 − 5.
= −1 − 5
Start at −1.
Go down 5.
We land on −6.
= −6
So −x² + 5x is −6 when x = −1.
Let's look back.
First: put the numbers in.
Then: powers.
Then: times and divide.
Last: plus and minus.
Answer
= −6