Question

What are the exact solutions of x^2 = 4 − 7x?

x = x equals negative 7 plus or minus the square root of thirty-three all over 2

x = x equals negative 7 plus or minus the square root of sixty-five all over 2

x = x equals 7 plus or minus the square root of sixty-five all over 2

x = x equals 7 plus or minus the square root of thirty-three all over 2

Answer 1

@IMStuck

Answer 2

Setting it up in standard form we have\[x ^{2}+7x-4=0\]

Answer 3

Then we factor this one just like the last one. You know, when it asks you to find the solutions of a quadratic, what it is asking you to do is find where x = 0, which ARE the solutions of a quadratic equation, or in other words, where the graph goes through the x axis, if it does. So we continue on...

Answer 4

\[x=\frac{ -7\pm \sqrt{(-7)^{2}-4(1)(-4)} }{ 2(1) }\]

Answer 5

This simplifies to:\[x=\frac{ -7\pm \sqrt{49+16} }{2 }\]which further simplifies to\[x=\frac{ -7\pm \sqrt{65} }{ 2 }\]

Answer 6

So these are your two solutions, still in radical form:\[x=\frac{ -7+ \sqrt{65} }{ 2 },x=\frac{ -7-\sqrt{65} }{ 2 }\]

Answer 7

The square root of 65 = 8.06223 So here are our solutions and then we will round them:\[x=\frac{ -7+8.06223 }{ 2 },x=\frac{ -7-8.06223 }{ 2 }\]

Answer 8

So just positive and negative versions of the same answer.

Answer 9

Doing that math you get x= .531 and x= -7.531

Answer 10

Yes just positive and negatives. But as you can see, the answer are VERY different from one another!

Answer 11

your answer is the second choice down. They left the square root of 65 in the answer and used the plus/minus instead of solving it for both values.

Answer 12

Got this? I'm going on a bike ride with my son for a bit, but I'll be back soon; tag me if you need me, ok?

Answer 13

And as always and ever, TY for the medal! You just raised my SmartScore a point!

Answer 14

Thank you so much! And no problem. Lol