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Solve the quadratic equation x2 − 4x = 21 by factoring.

User Ryogi
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1 Answer

10 votes

Answer:


x=7, x=-3

Explanation:

Bring the 21 on the LHS:


x^2-4x-21=0

At this point we need to find two numbers whose product is -21, and whose sum is -4.

From the product we can tell that one has to be positive, and one is negative.

From the sum, we can tell that the greater of the two is negative.

At this point we look at the factors of 21: 1,3,7,21.

In particular, 3 and -7 added togheter do -4, which is what we need. At this point we can factor the trinomial as


(x-7)(x+3)=0

Considering that a product is zero if any of the factors is zero, it's:
x-7=0 \rightarrow x=7\\x+3=0 \rightarrow x=-3

User Lyxal
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