Since there is an x2, we can do this step first:
(x )(x )
For this question, we need to use the quadratic formula:
-b±√(b2-4ac)
-----------------
2a
Let me explain some of the symbols and letters first.
±- is the plus or minus sign. You will perform both separately when we reach this step.
√-is the square root sign.
The line above 2a is the division line.
The letter a represents the quantity of x2, which is 1 in this case
The letter b represents the quantity of x, which is 9 in this case
The letter c represents the quantity of 1, which is 16 in this case
Let's plug the numbers in, so your formula will look like this:
-9±√(92-4(1)(16))
-----------------
2(1)
Simplify:
-9±√((81)-(64))
----------------- =
2
-9±√(17)
----------------- =
2
-9±(4.1231)
----------------- =This is the part where we split off into plus or minus
2
-9+4.1231
----------------- =
2
-4.8769
----------------- =
2
-2.4384 (This is one part of your answers. Let's do the minus part now.)
-9-4.1231
----------------- =
2
-13.1231
----------------- =
2
-6.56155 (This is your second part of your answer. The factorization is below)
(x-2.4384)(x-6.56155)
x(6x - 11)
(x - 6)(x2 + 6x + 36)
With great difficulty not knowing if 6x and 27 are plus or minus
-x(x2 - 2)(x2 + 3)
x2+6x-7 = (x+7)(x-1) when factored
x2 - 6x - 16 = (x + 2)(x - 8)
16 + 6x - x2 = 16 + 8x - 2x - x2 = 8*(2 + x) - x*(2 + x) = (8 - x)*(2 + x)
x2 + 6x - 2 can not be factored
x^2+6x-16 (x+2)+(6x-16) x+8+x-16 (x+8)(x-2) here you go :)
x2 - 6x - 16 = (x - 8)(x + 2)
-x2 + 6x + 16 = -(x2 - 6x - 16) = -(x - 8)(x + 2) = -(8 - x)(x + 2)
x2-6x can be factored into x(x-6). Simply factor out the "x" from both factors.
4
x2 + 6x = 16=> x2 + 6x - 16 = 0=> x2 + 8x -2x - 16 = 0=> (x+8)(x-2) = 0=> x = -8 or x = 2So, the solutions of the quadratic equation x2 + 6x = 16 are -8 and 2.
If you mean: 8x2-56x-64 which becomes x2-7x-8 and is (x-8)(x+1) when factored
x2 - 6x = 16 ∴ x2 - 6x + 9 = 25 ∴ (x - 3)2 = 25 ∴ x - 3 = 25 ∴ x = 28
x2 + 6x + 8 = (x + 4)(x + 2)