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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