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8 votes
8 votes
X^2-7x-34=10

Please help me answer this question thank you

User Pinale
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1 Answer

22 votes
22 votes

Answer:

x = -4 or 11

Explanation:

You want the solutions to the equation x² -7x -34 = 10.

Factors

We can put this in standard form and factor it.

x² -7x -44 = 0 . . . . . . . subtract 10

(x -11)(x +4) = 0 . . . . . . factor

The solutions make the factors zero:

x -11 = 0 ⇒ x = 11

x +4 = 0 ⇒ x = -4

The solutions are x = -4 and x = 11.

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Additional comment

The product of binomial factors is ...

(x +a)(x +b) = x² +(a+b)x +ab

We can find the value of 'a' and 'b' by considering the factors of the constant, -44:

-44 = (-44)(1) = (-22)(2) = (-11)(4)

These last two factors, -11 and 4, have a sum of -7, matching the coefficient of x. Hence these values are the 'a' and 'b' in our factoring of the quadratic.

x² -7x -44 = (x -11)(x +4)

There are additional products that give -44, such as (-4)(11), but we are only interested in those that have a negative sum of factors. -4+11 = +7, so is not of interest for this problem.

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User AndrewWinn
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