Rewrite the equation by completing the square. {:[4x^(2)-12 x+9=0],[(x+◻)^(2)=◻]:}

Question

Rewrite the equation by completing the square.  {:[4x^(2)-12 x+9=0],[(x+◻)^(2)=◻]:}

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Identifying Coefficients: We start by identifying the coefficient of x^2, which is 4, and the coefficient of x, which is -12. The constant term is 9. The equation is already set to equal zero, which is the first step in completing the square.Factoring Out Coefficient: To complete the square, we need to factor out the coefficient of x^2 from the first two terms. In this case, we factor out 4 from 4x^2 and -12x. 4(x^2 - 3x) + 9 = 0Completing the Square: Next, we find the value that completes the square for the expression x^2 - 3x. To do this, we take half of the coefficient of x, which is -3/2, and square it, resulting in (3/2)^2 = 9/4.Adding and Subtracting Value: We add and subtract this value inside the parentheses to maintain the equality. Since we factored out a 4 at the beginning, we need to add and subtract 4 times the value that completes the square. 4(x^2 - 3x + 9/4 - 9/4) + 9 = 0Simplifying the Equation: Now we simplify the equation by combining like terms inside the parentheses and adjusting the constant term outside. 4(x^2 - 3x + 9/4) - 4(9/4) + 9 = 0Simplifying Constants: Simplify the constants outside the parentheses. 4(x^2 - 3x + 9/4) - 9 + 9 = 0 4(x^2 - 3x + 9/4) = 0Writing as Perfect Square Trinomial: The expression inside the parentheses is now a perfect square trinomial, which can be written as (x - 3/2)^2. 4(x - 3/2)^2 = 0Rewriting the Equation: Finally, we rewrite the equation in the completed square form. (x - 3/2)^2 = 0

Rewrite the equation by completing the square. $\newline$ $4x^{2}-12x+9=0$ $\newline$ $(x+\square)^{2}=\square$

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Rewrite the equation by completing the square.\newline4x2−12x+9=04x^{2}-12x+9=04x2−12x+9=0\newline(x+□)2=□(x+\square)^{2}=\square(x+□)2=□

Rewrite the equation by completing the square. $\newline$ $4x^{2}-12x+9=0$ $\newline$ $(x+\square)^{2}=\square$