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$Solve for x. Enter the solutions from least to greatest. {:[x^(2)+12 x+27=0],[" lesser "x=◻],[" greater "x=◻]:}$

Solve for $x$ . Enter the solutions from least to greatest. $\newline$ $\begin{array}{l} x^{2}+12 x+27=0 \\ \text { lesser } x=\square \\ \text { greater } x=\square \end{array}$

Full solution

Q. Solve for

x

. Enter the solutions from least to greatest.

\newline

\begin{array}{l} x^{2}+12 x+27=0 \\ \text { lesser } x=\square \\ \text { greater } x=\square \end{array}

Identify quadratic equation: Identify the quadratic equation to be solved. $\newline$ The given quadratic equation is $x^2 + 12x + 27 = 0$ . We need to find two numbers that multiply to $27$ and add up to $12$ .
Factor the quadratic equation: Factor the quadratic equation. $\newline$ To factor $x^2 + 12x + 27$ , we look for two numbers that multiply to $27$ (the constant term) and add up to $12$ (the coefficient of $x$ ). The numbers $3$ and $9$ satisfy these conditions because $3 \times 9 = 27$ and $3 + 9 = 12$ . $\newline$ So, we can write the equation as $(x + 3)(x + 9) = 0$ .
Solve for x using factored form: Solve for x using the factored form. $\newline$ We have $(x + 3)(x + 9) = 0$ . Set each factor equal to zero and solve for x: $\newline$ $x + 3 = 0$ or $x + 9 = 0$ .
Solve first equation $x + 3 = 0$ : Solve the first equation $x + 3 = 0$ . $\newline$ Subtract $3$ from both sides to isolate $x$ : $\newline$ $x + 3 - 3 = 0 - 3$ $\newline$ $x = -3$
Solve second equation $x + 9 = 0$ : Solve the second equation $x + 9 = 0$ . $\newline$ Subtract $9$ from both sides to isolate $x$ : $\newline$ $x + 9 - 9 = 0 - 9$ $\newline$ $x = -9$
Write solutions in ascending order: Write the solutions in ascending order. $\newline$ The solutions are $x = -9$ and $x = -3$ . Since $-9$ is less than $-3$ , the solutions in ascending order are $-9$ , $-3$ .