b^2 + 35 = −12b Solve each equation by factoring
I really need help with understanding this step by step, thank you. I am giving 40 points for this.

Answers

Answer 1

Answer:

[tex]b=-5, -7[/tex]

Step-by-step explanation:

We have the equation [tex]b^2+35=-12b[/tex] and we want to solve it by factoring.

First, let's move all the stuff to one side so that the other side is 0. So, let's add [tex]12b[/tex] to both sides. This yields:

[tex]b^2+12b+35=0[/tex]

Let's review how to factor. If we have an equation in the following form:

[tex]ax^2+bx+c=0[/tex]

Where a, b, and c are the coefficients of the variable (in our example, our variable is b), then we must find two numbers, p and q, such that:

[tex]pq=ac \text{ (p times q equals a times c) and}\\p+q=b \text{ (p plus q equals b)}[/tex]

Our equation can be rewritten as:

[tex](1)b^2+(12)b+(35)=0[/tex]

So, our a is 1, b is 12, and c is 35.

Therefore, we need to find two numbers that when multiplied together yields a(c) = 1(35) = 35 and we added together yields b = 12.

From here, we just have to guess and check. We can start by listing all the factors of 35. There aren't in fact that many:

[tex]35: 1\text{ and } 35, 5\text{ and } 7[/tex]

1 + 35 is 36, not 12. However, 5 + 7 is indeed 12. So, our two numbers p and q are 5 and 7.

Now what we've found our two numbers, we substitute the b term for our two numbers. We have:

[tex]b^2+12b+35=0[/tex]

We will substitute 12b for 5b + 7b:

[tex]b^2+5b+7b+35=0[/tex]

From here, we factor by grouping. From the first two terms, factor out a b:

[tex]b(b+5)+7b+35=0[/tex]

And from the last two terms, factor out a 7:

[tex]b(b+5)+7(b+5)=0[/tex]

Now, notice that both terms have a [tex](b+5)[/tex]. So, by using grouping or the reverse of the distribute property, we can write:

[tex](b+7)(b+5)=0[/tex]

Notice that if we distribute the left term into the right, we get [tex]b(b+5)+7(b+5)=0[/tex], so our equation is indeed equivalent.

So now we. have:

[tex](b+7)(b+5)=0[/tex]

We can now use the Zero Product Property to acquire:

[tex]b+7=0\text{ or } b+5=0[/tex]

Solve for b for each case. Therefore, the solutions of our equation are:

[tex]b=-7\text{ or } b=-5[/tex]

Notes:

If we can't find two numbers p and q that satisfy our conditions, this means that the equation cannot be factored. So, we will use alternative methods to solve our equation.


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Answers

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Answers

Answer:

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Answers

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Answers

The answer is (x-3) = 2 lol

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_________________________________

[tex]x + 9 = {x}^{2} - 6x + 9[/tex]

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OR

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[tex] x = 7[/tex]

_________________________________

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Subtract sides 9

[tex]x + 9 - 9 = - {x}^{2} + 6x - 9 - 9 \\ [/tex]

[tex]x = - {x}^{2} + 6x - 18 [/tex]

Subtract sides x

[tex]x - x = - {x}^{2} + 6x - 18 - x [/tex]

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Multiply sides by -1

[tex] {x}^{2} - 5x + 18 = 0 [/tex]

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Thus (( x = 0 )) is unacceptable.

+++++++++++++++++++++++++++++++++++++++

[tex]x = 7[/tex]

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[tex]4 = 4[/tex]

Thus (( x = 7 )) is the only solution for x.

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Done...

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Elisha is paid $280 a week plus commission of $15 per sale. This week, she 2oints wants to earn at least $635. Which inequality represents this inequality?? ​

Answers

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Step-by-step explanation

weekly pay (280) + commision per sale (15x)  ≥ goal (635)

i need HELP!
Model the following situation with an equation or inequality statement.

The quotient of forty-nine and a number is greater than or equal to seven.

Answers

49 ÷ x ≥ 7

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Answer:

i am not sure but according to me ans is d

Step-by-step explanation:

Ax+By=C

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I don’t know if this is what you’re looking for but I got 103040000

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HELPP plsss

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Answer:

Is non-linear

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Answers

Answer:

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Answers

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HAAAAALP PLEASE BRAINLIEST PLEASE TRY

Answers

Answer:

D.

Step-by-step explanation:

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