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Chat with our AI personalities
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)
That doesn't factor neatly. Applying the quadratic formula, we find two real solutions: -8 plus or minus 2 times the square root of 14.
x = -0.5166852264521173
x = -15.483314773547882
16 - x2 would be factored into (4-x) and (4+x)
To double-check, multiply the factors:
(4-x)(4+x) = 16 + 4x - 4x -x2 = 16 - x2
4x - 16 = 4 (x - 4)
Factor out the greatest common factor (GCF), which is 4, and divide 4x - 16 by 4 to get x - 4, making the answer 4 (x - 4).
There is a formula for the "difference of squares." In this case, the answer is
(4x + 1)(4x - 1)
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