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$Solve for x. Enter the solutions from least to greatest. {:[3x^(2)+3x-90=0],[" lesser "x=◻],[" greater "x=◻]:}$

Solve for $x$ . Enter the solutions from least to greatest. $\newline$ $\begin{array}{l} 3 x^{2}+3 x-90=0 \\ \text { lesser } x=\square \\ \text { greater } x=\square \end{array}$

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Solve a quadratic equation by factoring

Full solution

Q. Solve for

x

. Enter the solutions from least to greatest.

\newline

\begin{array}{l} 3 x^{2}+3 x-90=0 \\ \text { lesser } x=\square \\ \text { greater } x=\square \end{array}

Write Equation: Write down the given quadratic equation. $\newline$ $3x^2 + 3x - 90 = 0$ $\newline$ We need to solve for $x$ .
Factor GCF: Factor out the greatest common factor (GCF) if possible. $\newline$ The GCF of the coefficients $3x^2$ , $3x$ , and $-90$ is $3$ . Let's factor it out. $\newline$ $3(x^2 + x - 30) = 0$
Factor Quadratic Expression: Now we need to factor the quadratic expression $x^2 + x - 30$ . $\newline$ We are looking for two numbers that multiply to $-30$ and add up to $1$ (the coefficient of $x$ ). $\newline$ The numbers $6$ and $-5$ work because $6 \times (-5) = -30$ and $6 + (-5) = 1$ . $\newline$ So we can write the factored form as: $\newline$ $3(x + 6)(x - 5) = 0$
Solve for x (Part $1$ ): Set each factor equal to zero and solve for x. $\newline$ First, we set the factor $x + 6$ equal to zero: $\newline$ $x + 6 = 0$ $\newline$ Subtract $6$ from both sides: $\newline$ $x = -6$
Solve for x (Part $2$ ): Set the other factor $x - 5$ equal to zero: $\newline$ $x - 5 = 0$ $\newline$ Add $5$ to both sides: $\newline$ $x = 5$
Write Solutions: Write down the solutions in ascending order. $\newline$ The lesser value of $x$ is $-6$ , and the greater value of $x$ is $5$ .

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