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$Rewrite the equation by completing the square. {:[x^(2)-20 x+100=0],[(x+◻)^(2)=◻]:}$

Rewrite the equation by completing the square. $\newline$ $x^2-20x+100=0$ , $(x+\square)^2=\square$

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Solve a quadratic equation by completing the square

Full solution

Q. Rewrite the equation by completing the square.

\newline

x^2-20x+100=0

,

(x+\square)^2=\square

Given quadratic equation: We start with the given quadratic equation. $\newline$ $x^2 - 20x + 100 = 0$ $\newline$ We need to complete the square for the quadratic term and the linear term.
Completing the square: To complete the square, we need to find a number that, when added and subtracted to the equation, forms a perfect square trinomial with $x^2$ and $-20x$ . The coefficient of $x$ is $-20$ , so we take half of it, which is $-10$ , and then square it to get $100$ .
Recognizing a perfect square trinomial: We notice that the constant term in the equation is already $100$ , which is the number we need to complete the square. $\newline$ So, the equation $x^2 - 20x + 100$ already represents a perfect square trinomial.
Rewriting the equation as a squared binomial: We can rewrite the equation as a squared binomial. $\newline$ $(x - 10)^2 = 0$ $\newline$ This is the completed square form of the equation.

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Solve by completing the square.

\newline

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