# Solving Quadratic Equations by Factorising (3)

In this worksheet, students solve quadratic equations by factorising.

Key stage:  KS 4

Curriculum topic:  Algebra

Curriculum subtopic:  Solve Quadratic Equations by Factorising

Difficulty level:

### QUESTION 1 of 10

A quadratic expression can sometimes be factorised.  If the product of these factors is zero, it is easy to solve the associated quadratic equation.

We use the fact that, if ab = 0, then we know that either a = 0 or b = 0 (or both).

Example

Solve for x:

20x2 + 20x = 15

20x2 + 20x = 15

Subtract 15 from both sides so that the equation reads = 0.

20x2 + 20x -15 = 0

Notice that each term is divisible by 5, so divide each term by 5 to get

4x2 + 4x - 3 = 0

Factorise the left hand side.

(2x + 3) (2x - 1) = 0

If (2x + 3) (2x - 1) = 0

then either (2x + 3) = 0 or (2x - 1) = 0

Write each equation separately.

2x + 3 = 0                                   2x - 1 = 0

Subtract 3 from both sides.                  Add 1 to both sides.

2x + 3 - 3 = 0 - 3                        2x - 1 + 1 = 0 + 1

Simplify.

2x = -3                                        2x = 1

Divide both sides by 2.                        Divide both sides by 2

x = -3/2                                        x = 1/2

Solution is:

x = -1½ or x = ½

Solve the quadratic equation by selecting all the correct solutions below.

x2 + 2x = 15

x = -5

x = 2/3

x = 2½

x = 3

Solve the quadratic equation by selecting all the correct solutions below.

x2 + 10x = -16

x = -8

x = -3/2

x = 1½

x = -2

Solve the quadratic equation by selecting all the correct solutions below.

x2 - 24 = 5x

x = -⅓

x = -3

x = 8

x = ¾

Solve the quadratic equation by selecting all the correct solutions below.

x2 - 3x = -2

x = 1

x = 2

x = -½

x = -2

Solve the quadratic equation by selecting all the correct solutions below.

6x2 + 13x = 5

x = -6

x = ⅓

x = -2½

x = 6

Solve the quadratic equation by selecting all the correct solutions below.

x2 = 11x - 18

x = -9

x = 9

x = ⅓

x = 2

Solve the quadratic equation by selecting all the correct solutions below.

x2 = 54 - 3x

x = -18

x = 3

x = 6

x = -9

Solve the quadratic equation by selecting all the correct solutions below.

10x2 = 12 - 7x

x = -1½

x = -4.5

x = ½

x = 4/5

Solve the quadratic equation by selecting all the correct solutions below.

6 = 5x - x2

x = 2

x = 3

x = ⅓

x = -2

Solve the quadratic equation by selecting all the correct solutions below.

10 = -4x2 - 13x

x = 2

x = -1¼

x = -2

x = 4/5

• Question 1

Solve the quadratic equation by selecting all the correct solutions below.

x2 + 2x = 15

x = -5
x = 3
EDDIE SAYS
(x+5)(x-3)= 0
• Question 2

Solve the quadratic equation by selecting all the correct solutions below.

x2 + 10x = -16

x = -8
x = -2
EDDIE SAYS
(x+8)(x+2)= 0
• Question 3

Solve the quadratic equation by selecting all the correct solutions below.

x2 - 24 = 5x

x = -3
x = 8
EDDIE SAYS
(x-8)(x+3)= 0
• Question 4

Solve the quadratic equation by selecting all the correct solutions below.

x2 - 3x = -2

x = 1
x = 2
EDDIE SAYS
(x-1)(x-2)= 0
• Question 5

Solve the quadratic equation by selecting all the correct solutions below.

6x2 + 13x = 5

x = ⅓
x = -2½
EDDIE SAYS
(3x-1)(2x+5)= 0
• Question 6

Solve the quadratic equation by selecting all the correct solutions below.

x2 = 11x - 18

x = 9
x = 2
EDDIE SAYS
(x-9)(x-2)= 0
• Question 7

Solve the quadratic equation by selecting all the correct solutions below.

x2 = 54 - 3x

x = 6
x = -9
EDDIE SAYS
(x+9)(x-6)= 0
• Question 8

Solve the quadratic equation by selecting all the correct solutions below.

10x2 = 12 - 7x

x = -1½
x = 4/5
EDDIE SAYS
(5x-4)(2x+3)= 0
• Question 9

Solve the quadratic equation by selecting all the correct solutions below.

6 = 5x - x2

x = 2
x = 3
EDDIE SAYS
(x-2)(x-3)= 0
• Question 10

Solve the quadratic equation by selecting all the correct solutions below.

10 = -4x2 - 13x

x = -1¼
x = -2
EDDIE SAYS
(4x+5)(x+2)= 0
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