SOLUTION: Solve the equation by completing the square x^2 + 4x - 21 = 0
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-> SOLUTION: Solve the equation by completing the square x^2 + 4x - 21 = 0
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Question 100954
:
Solve the equation by completing the square
x^2 + 4x - 21 = 0
Answer by
jim_thompson5910(35256)
(
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):
You can
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Start with the given equation
Add 21 to both sides
Take half of the x coefficient 4 to get 2 (ie
)
Now square 2 to get 4 (ie
)
Add this result (4) to both sides. Now the expression
is a perfect square trinomial.
Factor
into
(note: if you need help with factoring, check out this
solver
)
Combine like terms on the right side
Take the square root of both sides
Subtract 2 from both sides to isolate x.
So the expression breaks down to
or
or
Take the square root of 25 to get 5
or
Now combine like terms
So our answer is
or
Here is visual proof
graph of
Here we can see that the x-intercepts are
and
, so this verifies our answer.