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

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

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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}+2x

?

Identify Trinomial Form: To form a perfect square trinomial starting with $x^2 + 2x$ , we need to find a constant term $(c)$ such that the trinomial can be expressed as $(x + b)^2$ , where the linear coefficient $(2b)$ is equal to $2x$ .
Find Linear Coefficient: The linear coefficient in the expression $x^2 + 2x$ is $2$ . To find the constant term, we use the relationship $2b = 2$ , which implies that $b = 1$ .
Calculate Constant Term: Knowing that $b = 1$ , we can find the constant term by squaring $b$ . The constant term $c$ will be $b^2$ , which is $1^2$ .
Finalize Perfect Square Trinomial: Calculating the square of $b$ gives us $c = 1^2 = 1$ .

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