Rewrite the function by completing the square. {:[g(x)=x^(2)+15 x+54],[g(x)=◻(x+◻)^(2)+◻]:}

Identify coefficients: Identify the quadratic and linear coefficients in the function g(x). The quadratic coefficient is the coefficient of x^2, which is 1. The linear coefficient is the coefficient of x, which is 15.Complete the square: Divide the linear coefficient by 2 and square the result to find the number to complete the square. (15/2)^2 = 7.5^2 = 56.25Add and subtract: Add and subtract the number found in Step 2 inside the function to complete the square. g(x) = x^2 + 15x + 56.25 - 56.25 + 54Group and factor: Group the perfect square trinomial and the constants. g(x) = (x^2 + 15x + 56.25) - 56.25 + 54Combine constants: Factor the perfect square trinomial. g(x) = (x + 7.5)^2 - 56.25 + 54Combine the constants to simplify the function. g(x) = (x + 7.5)^2 - 2.25

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Algebra 1

Powers with decimal and fractional bases

Full solution

Q. Rewrite the function by completing the square.

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\begin{array}{l} g(x)=x^{2}+15 x+54 \\ g(x)=\square(x+\square)^{2}+\square \end{array}

Identify coefficients: Identify the quadratic and linear coefficients in the function $g(x)$ . $\newline$ The quadratic coefficient is the coefficient of $x^2$ , which is $1$ . The linear coefficient is the coefficient of $x$ , which is $15$ .
Complete the square: Divide the linear coefficient by $2$ and square the result to find the number to complete the square. $\newline$ $(\frac{15}{2})^2 = 7.5^2 = 56.25$
Add and subtract: Add and subtract the number found in Step $2$ inside the function to complete the square. $\newline$ g(x) = $x^2 + 15x + 56.25 - 56.25 + 54$
Group and factor: Group the perfect square trinomial and the constants. $\newline$ $g(x) = (x^2 + 15x + 56.25) - 56.25 + 54$
Combine constants: Factor the perfect square trinomial. $\newline$ g(x) = $(x + 7.5)^2 - 56.25 + 54$
Combine constants: Factor the perfect square trinomial. $\newline$ g(x) = (x + $7$ . $5$ )^ $2$ - $56$ . $25$ + $54$ Combine the constants to simplify the function. $\newline$ g(x) = (x + $7$ . $5$ )^ $2$ - $2$ . $25$