Solve each quadratic equation by factoring and using the zero product property.

10x + 6 = - 2x^2 - 2

x = - 4 or x = - 1

Step-by-step explanation:

Given equation is:

10x+6 = - 2x²-2

Adding 2x² and 2 to both sides of above equation, we get

2x²+2 + 10x+6 = - 2x²-2 + 2x²+2

Adding like terms, we get

2x²+10x+8 = 0

As we have noticed that there are multiples of 2.

Taking 2 as common, we get

2 (x²+5x+4) = 0

Multiplying by 1/2 to both sides of above equation, we get

1/2.2 (x²+5x+4) = 1/2.0

x²+5x+4 = 0

Split the middle term of above equation so that the sum of two term should be 5 and their product be 4.

x²+4x+x+4 = 0

Making two groups, we get

x (x+4) + 1 (x+4)

Taking (x+4) common, we get

(x+4) (x+1) = 0

Applying Zero-Product Property to above equation, we get

x+4 = 0 or x+1 = 0

Firstly, solve x+4 = 0

Adding - 4 to both sides of above equation, we get

x+4-4 = 0-4

x + 0 = - 4

x = - 4

Secondly, solve x+1 = 0

Adding - 1 to both sides of above equation, we get

x+1-1 = 0-1

x = - 1

Hence, the solution of 10x+6 = - 2x²-2 is {-4,-1}.

x = - 4 x=-1

Step-by-step explanation:

10x + 6 = - 2x^2 - 2

Add 2x^2 to each side

+2x^2 + 10x + 6 = 2x^2 - 2x^2 - 2

2x^2 + 10x + 6 = - 2

Add 2 to each side

2x^2 + 10x + 6+2 = - 2+2

2x^2 + 10x + 8 = 0

Divide each side by 2

2/2x^2 + 10/2x + 8/2 = 0/2

x^2 + 5x+4 = 0

What 2 numbers multiply to 4 and add to 5

4*1 = 4

4+1 = 5

(x+4) (x+1) = 0

Using the zero product property

x+4 = 0 x+1 = 0

x+4-4 = 0-4 x+1-1 = 0-1

x = - 4 x=-1