Hello aiwil.
11·x2 +88·x +176 = 0
Each of those numbers is a multiple of 11.
11·1·x2 +11·8·x +11·16 = 0
In other words, 11 is a common factor in each term. That means we can "pull out" the common factor, and write it in front of what's left.
11(x2 +8x +16) = 0
The next step is to factor the quadratic polynomial (x2+8x+16).
When we try to factor a polynomial in the form Ax2+Bx+C, we firstr look for two numbers (I'll call them 'number1' and 'number2') whose product is C and whose sum is B. That is, we're hoping to find two numbers so that
number1 × number2 = 16
number1 + number2 = 8
The polynomial's factorization then takes the form
Ax2 + Bx + C = (x + number1)(x + number2)
With a little thought, we realize the two numbers are 4 and 4 because
4 × 4 = 16
4 + 4 = 8
Therefore, the quadratic polynomial factors as (x+4)(x+4), and we can write that as (x+4)2.
(x + 4)2 equals zero when x+4 is zero.
x + 4 = 0
Subtract 4 from each side.
x + 4 - 4 = 0 - 4
x = -4
Questions?
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