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.)

4

Step-by-step explanation:

I took the test and got it right.