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What is the missing constant term in the perfect square that starts with
x^(2)+14 x ?

What is the missing constant term in the perfect square that starts with $x^{2}+14x$ ?

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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}+14x

?

Calculate Constant Term: To form a perfect square trinomial from the expression $x^2 + 14x$ , we need to find a constant term (let's call it $c$ ) such that the trinomial can be expressed as $(x + b)^2$ , where $b$ is half of the coefficient of $x$ . This means we need to take half of $14$ , which is $7$ , and then square it to find the constant term $c$ . $\newline$ Calculation: $(\frac{14}{2})^2 = 7^2 = 49$
Write Perfect Square Trinomial: Now that we have calculated the value of $c$ as $49$ , we can write the perfect square trinomial as $x^2 + 14x + 49$ . This trinomial is the square of the binomial $(x + 7)$ , because $(x + 7)^2 = x^2 + 2\times(7)\times x + 7^2$ , which simplifies to $x^2 + 14x + 49$ .

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