Completing the Square (Edexcel GCSE Maths): Flashcards

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Completing the Square
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What technique transforms quadratics into perfect square form?

Completing the square

Standard quadratic form

ax2+bx+cax^2 + bx + c

Completed square format with constants pp, qq

(x+p)2+q(x + p)^2 + q

Step 2: Divide coefficient of xx by? Then write?

2, then write (x + rac{b}{2})^2

Purpose of Step 4 adjusting number

Adjust constant to match original expression

Most common completing the square error

Forgetting the adjusting number

x2+8x+5x^2 + 8x + 5 in completed square form

(x+4)211(x + 4)^2 - 11

To solve after completing square, first...

Move constant to other side

Taking square root of both sides gives

pmpm solutions

Adjusting number formula (when a=1a=1)

c - ( rac{b}{2})^2

When to use: quadratic doesn't...

Factorise easily

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