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What is the missing constant term in the perfect square that starts with
x^(2)-20 x ?

What is the missing constant term in the perfect square that starts with $x^{2}-20x$ ?

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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}-20x

?

Identify general form: Identify the general form of a perfect square trinomial. A perfect square trinomial is an expression of the form $(ax + b)^2 = a^2x^2 + 2abx + b^2$ , where $a$ and $b$ are constants.
Recognize given expression: Recognize that the given expression $x^2 - 20x$ is the beginning of a perfect square trinomial, and it represents the $a^2x^2$ and $2abx$ parts of the general form. Here, $a = 1$ since the coefficient of $x^2$ is $1$ , and $-20$ is the result of $2ab$ .
Calculate value of : Calculate the value of by using the relationship $2$ ab = $-20$ . Since a = $1$ , we have $2$ ( $1$ )b = $-20$ , which simplifies to $2$ b = $-20$ .
Solve for b: Solve for b by dividing both sides of the equation $2b = -20$ by $2$ . This gives us $b = -20 / 2$ , which simplifies to $b = -10$ .
Find constant term: Find the constant term of the perfect square trinomial by squaring the value of $b$ . Since $b = -10$ , the constant term is $b^2 = (-10)^2$ .
Calculate $b^2$ : Calculate the value of $b^2$ . We have $(-10)^2 = 100$ .

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