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$Rewrite the equation by completing the square. {:[x^(2)+4x=0],[(x+◻)^(2)=◻]:}$

Rewrite the equation by completing the square. $\newline$ $x^2+4x=0$ $\newline$ $(x+\square)^2=\square$

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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+4x=0

\newline

(x+\square)^2=\square

Start with equation: Start with the given equation. $\newline$ Given equation: $x^2 + 4x = 0$ $\newline$ We want to complete the square for the left side of the equation.
Find value to complete square: Find the value needed to complete the square. $\newline$ To complete the square, we need to add $(\frac{b}{2})^2$ to both sides of the equation, where $b$ is the coefficient of $x$ . $\newline$ Here, $b = 4$ , so $(\frac{4}{2})^2 = 2^2 = 4$ .
Add value to both sides: Add the value to both sides of the equation. $\newline$ Add $4$ to both sides of the equation to complete the square on the left side. $\newline$ $x^2 + 4x + 4 = 0 + 4$
Factor the left side: Factor the left side of the equation. $\newline$ The left side of the equation is now a perfect square trinomial. $\newline$ $x^2 + 4x + 4$ can be factored into $(x + 2)^2$ .
Write completed square equation: Write the completed square equation. $\newline$ The equation after completing the square is: $\newline$ $(x + 2)^2 = 4$

More problems from Solve a quadratic equation by completing the square

Question

Solve by completing the square.

\newline

m^2 - 10m - 29 = 0

\newline

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g(x)

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What is the range of this quadratic function?

\newline

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\newline

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x

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