If you have to solve a quadratic equation but are not told which method to use, here is a guide as to what to do

** **

- When the question asks to
**solve by factorisation**

- For example, part (a) Factorise 6
*x*^{2}+ 7*x*– 3, part (b) Solve 6*x*^{2}+ 7*x*– 3 = 0

- For example, part (a) Factorise 6
- When solving
**two-term quadratic equations**- For example, solve
*x*^{2}– 4*x*= 0- …by taking out a
**common factor**of*x*to get*x*(*x*– 4) = 0 - ...giving
*x*= 0 and*x*= 4

- …by taking out a
- For example, solve
*x*^{2}– 9 = 0- …using the
**difference of two squares**to factorise it as (*x*+ 3)(*x*– 3) = 0 - ...giving
*x*= -3 and*x*= 3 - (Or by rearranging to
*x*^{2}= 9 and using ±√ to get*x*= = ±3)

- …using the

- For example, solve

** **

- When the question says to leave solutions correct to
**given accuracy**(2 decimal places, 3 significant figures etc) - When the quadratic formula may be
**faster**than factorising

- It's quicker to solve 36
*x*^{2}+ 33*x*– 20 = 0 using the quadratic formula then by factorisation

- It's quicker to solve 36
**If in doubt**, use the quadratic formula - it always works

** **

- When part (a) of a question says to
**complete the square**and part (b) says to use part (a) to solve the equation - When making
*x*the**subject of harder formulae**containing*x*^{2}and*x*terms- For example, make
*x*the subject of the formula*x*^{2}+ 6*x*=*y*- Complete the square: (
*x*+ 3)^{2}– 9 =*y* - Add 9 to both sides: (
*x*+ 3)^{2}=*y*+ 9 - Take square roots and use ±:
- Subtract 3:

- Complete the square: (

- For example, make

- Calculators can solve quadratic equations so use them to check your solutions
- If the solutions on your calculator are whole numbers or fractions (with no square roots), this means the quadratic equation does factorise

(a)

Solve , giving your answers correct to 2 decimal places

“Correct to 2 decimal places” suggests using the quadratic formula

Substitute *a* = 1, *b* = -7 and *c* = 2 into the formula, putting brackets around any negative numbers

Use a calculator to find each solution

*x* = 6.70156… or 0.2984...

Round your final answers to 2 decimal places

*x*** = 6.70 or x = 0.30**

(b)

Solve

__Method 1__

If you cannot spot the factorisation, use the quadratic formula

Substitute* a* = 16, *b* = -82 and *c *= 45 into the formula, putting brackets around any negative numbers

Use a calculator to find each solution

*x*** = **** or x = **

__Method 2__If you do spot the factorisation, (2x – 9)(8x – 5), then use that method instead

Set the first bracket equal to zero

Add 9 to both sides then divide by 2

Set the second bracket equal to zero

Add 5 to both sides then divide by 8

*x*** = **** or x = **

(c)

By writing in the form , solve

This question wants you to complete the square first

Find *p* (by halving the middle number)

Write *x*^{2} + 6*x* as (*x* + *p*)^{2} - *p*^{2 }

Replace *x*^{2} + 6*x *with (*x* + 3)^{2} – 9 in the equation

Make *x* the subject of the equation (start by adding 4 to both sides)

Take square roots of both sides (include a ± sign to get both solutions)

Subtract 3 from both sides

Find each solution separately using + first, then - second

*x*** = - 5, x = - 1**

Even though the quadratic factorises to (*x *+ 5)(*x* + 1), this is not the method asked for in the question

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