Answer
The answer is $[-5,2]$.
Work Step by Step
The given expression is
$x^2+3x\leq10$.
Express the inequality in the form $f(x)\leq0$.
$x^2+3x\leq10$.
Subtract $10$ from both sides.
$x^2+3x-10\leq10-10$.
Simplify.
$x^2+3x-10\leq0$.
Factors are.
$x^2+5x-2x-10\leq0$.
$x(x+5)-2(x+5)\leq0$.
$(x+5)(x-2)\leq0$
Set each factor equal to zero.
$x+5=0$ and $x-2=0$.
Isolate $x$.
$x=-5$ and $x=2$.
The solution set is $[-5,2]$.
