Question
Find the value of 2x² + 3x - 1 when x = 2.
Solution — Step by Step
We have 2x² + 3x - 1 and we need to put x = 2 everywhere we see x. Every single x gets replaced — don’t miss any.
x² means x × x. So when x = 2, we get 2² = 2 × 2 = 4. Then the coefficient gives us 2 × 4 = 8.
3x with x = 2 gives 3 × 2 = 6. Straightforward multiplication.
The final answer is 13.
Why This Works
Substitution is the most fundamental operation in algebra — we’re treating the expression as a machine. You feed in a value of x, and the expression spits out a number.
The reason we handle each term separately before adding is BODMAS. We must deal with the exponent (x²) and then the multiplication (by 2 and by 3) before doing any addition or subtraction.
This same process is used all the way from Class 7 through Class 12. When you verify roots of a quadratic or check whether a value satisfies an equation, you’re doing exactly this.
Alternative Method — Box Substitution
If you’re prone to missing an x somewhere, rewrite the expression with a box first:
Replace every x with a ☐, then fill in 2:
This sounds childish but it’s actually used by toppers to avoid silly mistakes under exam pressure. A mark lost to substitution error is the most frustrating mark to lose.
Common Mistake
The classic error here is writing 2x² = (2x)². These are very different things:
2x²withx = 2→2 × (2²)=2 × 4 = 8(2x)²withx = 2→(2 × 2)²=(4)²=16
The coefficient 2 is not inside the square. Only x is being squared. This single mistake has cost students marks in board exams more times than we can count.
To double-check your answer quickly: put x = 0 mentally. The expression becomes 2(0) + 3(0) - 1 = -1. If your substitution method gives -1 when you try x = 0, you know your process is right before tackling x = 2.