Question

solve the following equations

1. $x^{2}+3x - 10 = 0$

Explanation:

Step1: Factor the quadratic trinomial

Find two numbers that multiply to $-10$ and add to $3$: $5$ and $-2$.
$x^2 + 3x - 10 = (x+5)(x-2) = 0$

Step2: Apply zero product property

Set each factor equal to 0.
$x+5=0$ or $x-2=0$

Step3: Solve for $x$ in each equation

For $x+5=0$: $x = -5$; for $x-2=0$: $x=2$

Answer:

$x = -5$ or $x = 2$