Completing the Square (Grade 11 NSC Matric Mathematics): Quizzes

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Completing the Square
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What is the main purpose of completing the square?

To solve quadratics that can't be factorised

When is completing the square particularly useful?

To find exact irrational solutions

What is Step 2 in completing the square?

Make the coefficient of x2x^2 equal to 1

In Step 3, what do you do with the coefficient of xx?

Take half of it and square it

After completing the square, which two methods can you use to solve?

Square root method or difference of squares

For x2−10x−11=0x^2 - 10x - 11 = 0, what value must be added and subtracted in Step 3?

25

What is the perfect square form of x2−10x+25−36=0x^2 - 10x + 25 - 36 = 0?

(x−5)2−36=0(x - 5)^2 - 36 = 0

What critical symbol must you always remember when taking square roots?

The ± sign

For 2x2−6x−10=02x^2 - 6x - 10 = 0, what must you do first?

Divide entire equation by 2

When are solutions irrational in completing the square?

When there's no perfect square under the root

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