Simplify completely. 5(x

Solve the equations for all values of x by completing the square x^2+62=-16x

lorasvet [3.4K]

Answer:

$x = \sqrt{2} - 8\\x = -\sqrt{2} - 8$

Step-by-step explanation:

To complete the square, we first have to get our equation into $ax^2 + bx = c$ form.

First we add 16x to both sides:

$x^2 + 16x + 62 = 0$

And now we subtract 62 from both sides.

$x^2 + 16x = -62$

We now have to add $(\frac{b}{2})^2$ to both sides of the equation. b is 16, so this value becomes $(16\div2)^2 = 8^2 = 64$ .

$x^2 + 16x + 64 = -62+64$

We can now write the left side of the equation as a perfect square. We know that x+8 will be the solution because $8\cdot8=64$ and $8+8=16$ .

$(x+8)^2 = -62 + 64$

We can now take the square root of both sides.

$x+8 = \sqrt{-62+64}\\\\ x+8 = \pm \sqrt{2}$

We can now isolate x on one side by subtracting 8 from both sides.

$x = \pm\sqrt{2} - 8$

So our solutions are

$x = \sqrt{2} - 8\\x = -\sqrt{2} - 8$

Hope this helped!

4 0

3 years ago

Mark has $16 to buy lunch for himself and his sister. He wants to buy at least one sandwich and one bag of chips. Sandwiches cos

faltersainse [42]

Answer:

Victor runs a small sandwich shop. He decides to start offering bags of chips to his customers. He finds a supplier where he can buy chips for $0.30 per bag. Victor needs to determine how much to charge for the chips at his shop. He does some research by talking to other nearby sandwich shop owners. The table below shows their sales per week for two different prices. (The values are: 150 bags sold, for $1.00 per bag, and 350 bags sold, for $0.50 per bag.) Victor believes that there is a linear relationship between the number of bags sold and the price. Victor wants to price the bags of chips so that he will maximize his profits. Determine the price Victor should charge for a bag of chips. Use the equation P(x)=R(x)-C(x), where P(x) represents profit, R(x) represents revenue, and C(x) represents cost. Each is a function of the number of bags of chips sold, x. Round your answer to the nearest nickel.

Step-by-step explanation:

Victor runs a small sandwich shop. He decides to start offering bags of chips to his customers. He finds a supplier where he can buy chips for $0.30 per bag. Victor needs to determine how much to charge for the chips at his shop. He does some research by talking to other nearby sandwich shop owners. The table below shows their sales per week for two different prices. (The values are: 150 bags sold, for $1.00 per bag, and 350 bags sold, for $0.50 per bag.) Victor believes that there is a linear relationship between the number of bags sold and the price. Victor wants to price the bags of chips so that he will maximize his profits. Determine the price Victor should charge for a bag of chips. Use the equation P(x)=R(x)-C(x), where P(x) represents profit, R(x) represents revenue, and C(x) represents cost. Each is a function of the number of bags of chips sold, x. Round your answer to the nearest nickel.

4 0

3 years ago

Mercedes is helmet diving at a location of -20 feet. The breathing tube attached to her helmet reaches an oxygen tank at a locat

-BARSIC- [3]

Answer: B

Step-by-step explanation:

6 0

3 years ago

What ordered pair is a solution of the equation?<br><br> y=-2x-5

ioda

$\sf \underline{Answer:}$

Pick any value for x, like x = 0, plug it into the equation, and get the value for y. For x = 0,

2(0) + y = 5

y = 5

The ordered pair is (0,5). Find other ordered pairs using the same reasoning.

3 0

2 years ago

Read 2 more answers

I don't know what's it asking me. what should I do?

Anton [14]

$n$ - a number
$n^2$ - its square
$n+n^2$ - the sum
$\leq$ - less than or equal
negative three - I don't have to explain this one, do I?

$n+n^2\leq-3$ - the sum of a number and its square is less than or equal negative three

6 0

3 years ago

Read 2 more answers

Simplify completely. 5(x - 2) + 2x