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What is the missing constant term in the perfect square that starts with
x^(2)-12 x ?

What is the missing constant term in the perfect square that starts with $x^{2}-12x$ ?

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Solve a quadratic equation by completing the square

Full solution

Q. What is the missing constant term in the perfect square that starts with

x^{2}-12x

?

Find the Perfect Square Trinomial: To complete the square for the expression $x^2 - 12x$ , we need to find a number that, when added to the expression, turns it into a perfect square trinomial. The formula for a perfect square trinomial is $(x - a)^2 = x^2 - 2ax + a^2$ , where $a$ is the number we are looking for.
Determine the Value of 'a': The coefficient of $x$ in our expression is $-12$ , so in the formula $-2ax$ , $a$ would be half of $-12$ , which is $-6$ . This is because $-2 \times (-6)$ gives us the $-12$ we have in our original expression.
Square the Value of 'a': Now we need to square the value of $a$ to get the constant term. So we square $-6$ to get $36$ .
Add the Constant Term: The constant term needed to complete the square is $36$ . Adding this to our expression $x^2 - 12x + 36$ will result in a perfect square trinomial.

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