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$Solve for x. Enter the solutions from least to greatest. {:[x^(2)+18 x+80=0],[" lesser "x=◻],[" greater "x=◻]:}$

Solve for $x$ . Enter the solutions from least to greatest. $\newline$ $\begin{array}{l} x^{2}+18 x+80=0 \\ \text { lesser } x=\square \\ \text { greater } x=\square \end{array}$

Full solution

Q. Solve for

x

. Enter the solutions from least to greatest.

\newline

\begin{array}{l} x^{2}+18 x+80=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 $x^2 + 18x + 80 = 0$ . We need to find two numbers that multiply to $80$ and add up to $18$ .
Factor the quadratic equation: Factor the quadratic equation. $\newline$ To factor $x^2 + 18x + 80$ , we look for two numbers that multiply to $80$ (the constant term) and add up to $18$ (the coefficient of the $x$ term). The numbers $10$ and $8$ satisfy these conditions because $10 \times 8 = 80$ and $10 + 8 = 18$ . $\newline$ So, we can write the equation as $(x + 10)(x + 8) = 0$ .
Solve for x using factored form: Solve for x using the factored form. $\newline$ We have $(x + 10)(x + 8) = 0$ . Set each factor equal to zero and solve for x: $\newline$ $x + 10 = 0$ or $x + 8 = 0$ .
Solve first equation: Solve the first equation $x + 10 = 0$ . $\newline$ Subtract $10$ from both sides to isolate $x$ : $\newline$ $x + 10 - 10 = 0 - 10$ $\newline$ $x = -10$
Solve second equation: Solve the second equation $x + 8 = 0$ . $\newline$ Subtract $8$ from both sides to isolate $x$ : $\newline$ $x + 8 - 8 = 0 - 8$ $\newline$ $x = -8$
Write solutions in ascending order: Write the solutions in ascending order. $\newline$ The solutions are $x = -10$ and $x = -8$ . In ascending order, the solutions are $-10$ , $-8$ .