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$Rewrite the equation by completing the square. {:[4x^(2)+8x+3=0],[(x+◻)^(2)=◻]:}$

Rewrite the equation by completing the square. $\newline$ $4x^{2}+8x+3=0$ $\newline$ $(x+\square)^{2}=\square$

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Solve a quadratic equation by completing the square

Full solution

Q. Rewrite the equation by completing the square.

\newline

4x^{2}+8x+3=0

\newline

(x+\square)^{2}=\square

Divide by $4$ : First, divide the entire equation by $4$ to make the coefficient of $x^2$ equal to $1$ . $\newline$ $x^2 + 2x + \left(\frac{3}{4}\right) = 0$
Complete the square: Next, to complete the square, we need to add and subtract $(b/2)^2$ , where $b$ is the coefficient of $x$ . In this case, $b = 2$ , so $(b/2)^2 = (2/2)^2 = 1$ . Add and subtract $1$ inside the equation. $x^2 + 2x + 1 - 1 + (3/4) = 0$
Combine constants: Now, combine the constants on the right side of the equation. $\newline$ $x^2 + 2x + 1 = 1 - \frac{3}{4}$
Simplify equation: Simplify the right side of the equation. $x^2 + 2x + 1 = \frac{1}{4}$
Write as binomial square: Write the left side of the equation as a square of a binomial. x + \(1)^ $2$ = \frac{ $1$ }{ $4$ }\
Rewrite equation: The equation is now rewritten by completing the square. x + \(1)^ $2$ = \frac{ $1$ }{ $4$ }\

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