Question

Solve by factoring
**Must be in standard form: ax+bx+c=0
2x²+2x-4=0
​

Answer 1

x = 1 or x = -2

Explanation:

solve by factoring

2xx +2x - 4 =0

First factor out 2

2( xx + x - 2) = 0

2( xx + x + (1/2)^2 - (1/2)^2 - 2) = 0

2(xx + x + (1/2)^2 - 1/4-2 ) = 0

2( (x + 1/2)^2 -9/4 ) = 0

2 (x +1/2)^2 - 9/2 =0

2 (x +1/2)^2 =9/2

(x +1/2)^2 = 9/4

x + 1/2 = 3/2 or x +1/2 = -3/2

x = 1 or x =-2

Answer 2

x = 1 or -2

Explanation:

Given the equation:

`\sf 2x^2 + 2x - 4 = 0`

We can factor out the common factor of 2 from all the terms: x = 1 or -2.

`\sf 2(x^2 + x - 2) = 0`

Now, let's simplify further by factoring the quadratic expression by middle term factorization:

`\sf 2(x^2 + x - 2) = 0`

We can write it as:

`\sf 2(x^2 + (2-1) x - 2) = 0`

`\sf 2(x^2 + 2x - x - 2 )= 0`

Now, factor by grouping:

`\sf2((x^2 + 2x) - (x + 2)) = 0`

Now, factor out common terms from each group:

`\sf2( x(x + 2) - 1(x + 2)) = 0`

Now, we have a common factor of (x + 2) in both terms:

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

So, the quadratic equation in standard form is:

`\sf 2(x - 1)(x + 2) = 0`

Either,

(x-1)=0

x=1

or

(x+2)=0

x=-2,

Therefore, x = 1 or -2.