Question

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

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

Answer 1

x = -4 or x = -1

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}.

Answer 2

x = -4 x=-1

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