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<h3>Answer: x = -5, -4, 4 and 5.</h3><h3>All four zeros are real solutions.</h3>
Step-by-step explanation:
Given the polynomial equation .
Adding 400 on both sides to get rid 400 from right side and set 0 on right side, we get
.
.
Factoring by product sum rule.
We need product of 400 and sum upto -41.
We can see that 400 = -25 × -16 = 400 and -25-16 = -41.
Therefore,
Making it into two groups, we get
Factoring out GCF of each group, we get
Factoring out and
separately by difference of the squares identity
, we get
and
.
Therefore,
Applying zero product rule,
x-5=0
x+5=0
x-4=0 and
x+4=0.
Therefore,
<h3>x = -5, -4, 4 and 5.</h3><h3>All four zeros are real solutions.</h3>