Answer:
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.)
