Question

question 2 of 10 which of the following are solutions to the equation below? check all that apply. 2x² + 6x = 20 a. -2 b. -5 c. -10 d. 20 e. 2 f. 1

Explanation:

Step1: Rearrange the equation

First, rewrite the equation $2x^{2}+6x = 20$ in standard - quadratic form $ax^{2}+bx + c = 0$. Subtract 20 from both sides to get $2x^{2}+6x−20 = 0$. Then divide through by 2 to simplify: $x^{2}+3x - 10=0$.

Step2: Factor the quadratic equation

Factor the quadratic $x^{2}+3x - 10$. We need two numbers that multiply to - 10 and add up to 3. The numbers are 5 and - 2. So, $x^{2}+3x - 10=(x + 5)(x - 2)=0$.

Step3: Solve for x

Set each factor equal to zero:
If $x + 5=0$, then $x=-5$.
If $x - 2=0$, then $x = 2$.

Answer:

B. -5
E. 2