Quadratic equations and factoring

8x^2 + 10x+3=0

and completing the square

a^2-7a+c

1. - 3/4, - 1/2.

2. a = 3.5 + √ (12.25 - c), 3.5 - √ (12.25 - c)

Step-by-step explanation:

8x^2 + 10x + 3 = 0

Looks like we can solve this by the ac factoring method.

Here ac = first coefficient * the last = 8 * 3 = 24.

Now wee need 2 numbers whose product is + 24 and whose sum is + 10.

They are 6 and 4, so we write the equation as follows:

8x^2 + 4x + 6x + 3 = 0. Now we factor by grouping:

4x (2x + 1) + 3 (2x + 1) = 0 The 2x + 1 is common so:

(4x + 3) (2x + 1) = 0

x = - 3/4, x = - 1/2.

2. a^2 - 7a + c = 0

Completing the square:

(a - 3.5) ^2 - 3.5^2 + c = 0

(a - 3.5) ^2 - 12.25 = - c

(a - 3.5) ^2 = 12.25 - c

(a - 3.5) = + / - √ (12.25 - c)

a = 3.5 + √ (12.25 - c), 3.5 - √ (12.25 - c.)