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By the completion or non-completion
Puranapuranabhyam
By completion or non-completion — complete the square to simplify expressions. For x² + bx, add (b/2)² to form a perfect square trinomial. This technique is fundamental for solving quadratics and simplifying algebraic expressions.
How It Works
- 1.Start with an expression x² + bx (missing the constant to be a perfect square).
- 2.Take the coefficient of x, which is b.
- 3.Halve it: b/2.
- 4.Square the result: (b/2)².
- 5.Add this value to complete the square: x² + bx + (b/2)² = (x + b/2)².
Examples
x² + 8x + ? = 16
Step 1 / 5
Complete the square for x² + 8x + ___ .
Expressionx² + 8x + ?
Coefficient of x (b)8
Try It Yourself
x² + 20x + ? → missing value?