Question

Factorise
1. 4x² = 4x+11
2. x² +8 = 4x
3. 2x²-7x+3 = 0
4. 3x² +10x = 8
5. x² + 8x = -7
6. 2x² - 4x-6=0
7.6x² - x = 15​

Answer 1

Step-by-step explanation:

Solutions :-

1. )

Given equation is 4x^2= 4x+11

=> 4x^2-4x-11 = 0

=> 4x^2/4 -4x/4 - 11/4 = 0

=> x^2-x-11/4 = 0

=>x^2-(2/2)x =11/4

=> x^2-2(x)(1/2) = 11/4

=>x^2-2(x)(1/2)+(1/2)^2 = (11/4)+(1/2)^2

=>[x-(1/2)]^2 = (11/4)+(1/4)

=>[x-(1/2)]^2 =(11+1)/4

=> [x-(1/2)]^2 =12/4

=> [x-(1/2)]^2 = 3

=> x-(1/2) = ±√3

=> x = (1/2)±√3

=>x=(1±2√3)/2

=> x-(1±2√3)/2 = 0

=> [x-(1+2√3)/2][x-(1-2√3)/2]=0

=> [(2x-1-2√3)/2][(2x-1+2√3)/2]=0

=> (2x-1-2√3)(2x-1+2√3)=0

2. )

Given equation is x^2+8 = 4x

=> x^2+8-4x = 0

=> x^2-4x+8 = 0

=> x^2-2(x)(2) +8 = 0

=>x^2-2(x)(2)=-8

=>x^2-2(x)(2)+2^2=-8+2^2

=>(x-2)^2=-8+4

=>(x-2)^2=-4

=>x-2 = ±√-4

=>x = 2±√-4

=> (x-(2±√-4) )= 0

=>(x-2+√-4)(x-2-√-4) = 0

3. ) Given equation is 2x^2-7x+3 = 0

=> 2x^2-x-6x+3 = 0

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

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

4. )Given equation is 3x^2 +10x = 8

=> 3x^2+10x-8 = 0

=> 3x^2+12x-2x-8 = 0

=>3x(x+4)-2(x+4) = 0

=> (x+4)(3x-2) = 0

5.) Given equation is x^2 + 8x = -7

=> x^2+8x+7 = 0

=>x^2+x+7x+7 = 0

=>x(x+1)+7(x+1) = 0

=> (x+1)(x+7) = 0

6.) Given equation is 2x^2- 4x-6=0

=> 2(x^2-2x-3) = 0

=> x^2-2x-3 = 0

=>x^2+x-3x-3 = 0

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

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

7.) Given equation is 6x^2 - x = 15

=> 6x^2-x-15 = 0

=> 6x^2+9x-10x -15 = 0

=> 3x(2x+3)-5(2x+3) = 0

(2x+3)(3x-5) = 0

Used formulae:-

• Splitting the middle term

• Completing the square method

• (a+b)^2 = a^2+2ab+b^2

• (a-b)^2=a^2-2ab+b^2