Find the value of c such that the expression is a perfect-square trinomial.
xsquaredplus14xplusc
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Part 1
cequals
enter your response here
(Simplify your answer. Type an integer or a fraction.)
c = 49
Explanation:
To make xsquared + 14x + c a perfect-square trinomial, we need to find a number that, when squared, will give us the last term c. In this case, c = 49 (7^2) will make the expression a perfect-square trinomial.
Complete the square.
ysquaredminus12y
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Part 1
Find the missing term that completes the square.
ysquaredminus12yplus
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(Simplify your answer. Type an integer or a fraction.)
To complete the square for the expression y^2 - 12y, we need to find the term that, when squared, will give us the missing term.
To find this term, we take half of the coefficient of y (which is -12) and then square it.
Half of -12 is -6, and (-6)^2 = 36.
Therefore, the missing term that completes the square is 36.
The completed square expression is: y^2 - 12y + 36.
Find the value of c such that the expression is a perfect-square trinomial.
xsquaredplus8xplusc
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Part 1
cequals
enter your response here
(Simplify your answer. Type an integer or a fraction.)
To make x^2 + 8x + c a perfect-square trinomial, we need to find a number that, when squared, will give us the middle term 8x.
In this case, the number that completes the square is half of the coefficient of x (which is 8), squared.
Half of 8 is 4, and 4 squared is 16.
Therefore, the value of c that makes x^2 + 8x + c a perfect-square trinomial is c = 16.