Mathematics, 02.08.2019 10:30 Barbiealice8362

Let x^2+15x=49 what values make an equivalent number sentence after completing the square? enter your answers in the boxes. x² + 15x +

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x^2 + 15x + 56.25 = 105.25

"Completing the square" is one of many different techniques for solving a quadratic equation. What you do is add a constant to both sides of the equation such that the lefthand side can be factored into the form a(x+d)^2. For instance, squaring (X+D) = X^2 + 2DX + D^2. Notice the 2DX term. That is the same term as the 15x term in the problem. So 2D = 15, D = 7.5. And D^2 = 7.5^2 = 56.25.
So we have
x^2 + 15x + 56.25 = 49 + 56.25
Which is
x^2 + 15x + 56.25 = 105.25
Which is the answer desired.

Now the rest of this is going beyond the answer. Namely, it's answering the question "Why does complementing the square help?" Well, we know that the left hand side of the equation can now be written as
(x+7.5)^2 = 105.25

Now take the square root of each side
(x+7.5) = sqrt(105.25)

And let's use both the positive and negative square roots.
So x+7.5 = 10.25914226
and
x+7.5 = -10.25914226

And let's find X.
x+7.5 = 10.25914226
x = 2.759142264

x+7.5 = -10.25914226
x = -17.75914226

So the roots for x^2 + 15x - 49 is 2.759142264, and -17.75914226

Answer from: kcarstensen59070

The correct answer is:

x^2 + 15x + 56.25 = 105.25

i just finished the test and these were the correct answers :)

Answer from: Quest

the answer is 200

step-by-step explanation:

this is a problem about poisson probabilities. i don't know if you've

already studied poisson distributions, or if you have a place to look

to read more about the subject.

here's how you can see a poisson distribution coming. when there are

a lot of events that may happen at any time (or any place), and when

you're counting how many of them happen at a particular time (or a

particular place), and each event is independent of the others, then

the result is a poisson distribution. this is roughly true for the

chocolate chips; one chip being in a cookie has only a small effect on

the probability that another chip will be in the cookie.

once you know you have a poisson distribution, you know a lot. there

is only one parameter to a poisson distribution, so if you know the

mean, you know everything. the form of the distribution is

probability of n chips = {[e^(-x)]*(x^n)} / (n! )

Answer from: Quest

step-by-step explanation:

sry but any answer choices

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Let x^2+15x=49 what values make an equivalent number sentence after completing the square? enter yo...