question 9 solve algebraically for all values of x: 2x² - 8x - 10 = 0

Explanation:

Step1: Divide by 2

Divide the entire equation $2x^{2}-8x - 10=0$ by 2 to simplify. We get $x^{2}-4x - 5=0$.

Step2: Factor the quadratic

Factor $x^{2}-4x - 5$. We need two numbers that multiply to - 5 and add up to - 4. The numbers are - 5 and 1. So, $x^{2}-4x - 5=(x - 5)(x+1)=0$.

Step3: Solve for x

Set each factor equal to zero. If $x - 5=0$, then $x = 5$. If $x+1=0$, then $x=-1$.

Answer:

$x = 5,x=-1$