Question

What are the exact solutions of x2 − 3x − 7 = 0?

Answer 1

...

Answer 2

@friedch1cken , have you read the Code of Conduct?

Answer 3

D: Sorry

Answer 4

Yea, you're not supposed to do that...

Answer 5

You can show work to the second to last step though ;)

Answer 6

what about the code of conduct?

Answer 7

@StealerGirly50 , nothing to do with you; don't worry about it :)

Answer 8

oh ok

Answer 9

\[x^2 − 3x − 7 = 0\]
Okay, we can begin by completing the square. Let's move the constant term to the right. Add 7 to both sides of the equation.
\[x^2-3x-7+7 = 0 +7\]\[x^2-3x=7\] The x term is -3x. Take half its coefficient (1 1/2).
Square it (2 1/4) and add it to both sides. Add '2 1/4' to each side of the equation.
\[x^2 - 3x + 2.25= 7 +2 \frac{1}{4}\]
Combine like terms. 7 + 2 1/4 = 7 1/4
\[x^2 - 3x +2 \frac{1}{4} = 9 \frac{1}{4}\]
Factor a perfect square on the left side: \[(x -\frac{1}{2})(x - \frac{1}{2}) = 9 \frac{1}{4}\]
\[(x-\frac{1}{2})^2 = 9 \frac{1}{4}\]
We can take the square roots of both sides.
\[x - \frac{1}{2} = \pm \sqrt{9 \frac{1}{4}}\]
Now, we can set up two subproblems, one with a negative square root of 9.25 and the other with a positive square root of 9.25.
\[x-\frac{1}{2}=\sqrt{9 \frac{1}{4}}\]
Add 1/2 to both sides.
\[x = \frac{1}{2} + \sqrt{9 \frac{1}{4}}\]
Now we have one of our answers. We will solve the next subproblem, with a negative square root of 9/4 now.
\[x- \frac{1}{2} = -\sqrt{9\frac{1}{4}}\]
Add 1/2 to both sides.\[x = \frac{1}{2}-\sqrt{9\frac{1}{4}}\]
And there's your second answer. So, all in all,
\[x = \left\{ \frac{1}{2}-\sqrt{9\frac{1}{4}}, \frac{1}{2}+\sqrt{9 \frac{1}{4}} \right\}\]
Does that make sense?

Answer 10

Ya but what is supposed to be in the last (math processing error)

Answer 11

What's supposed to be where?