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What is the missing constant term in the perfect square that starts with
x^(2)+10 x ?

What is the missing constant term in the perfect square that starts with $x^{2}+10x$ ?

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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}+10x

?

Finding the Perfect Square Trinomial: To complete the square for an expression of the form $x^2 + bx$ , we need to find a number that can be added to make it a perfect square trinomial. The formula for the constant term in a perfect square trinomial is $(\frac{b}{2})^2$ .
Calculating the Constant Term: In the given expression $x^2 + 10x$ , the coefficient $b$ in front of $x$ is $10$ . To find the constant term, we need to divide $b$ by $2$ and then square the result.
Squaring the Result: Divide $10$ by $2$ to get $5$ . Then square $5$ to find the constant term. $\newline$ Calculation: $(\frac{10}{2})^2 = 5^2 = 25$ .
Completing the Perfect Square Trinomial: The missing constant term that would make $x^2 + 10x$ a perfect square is $25$ . Adding this term to the expression gives us $(x + 5)^2$ , which is the perfect square trinomial.

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