Question

Which of the following are solutions to the equation below? Check all that apply. 2x2 + 18 x = 20 A. 20 I B. 1 C. -2 O D. -2 E. -10 1 F. -1​

Answer 1

B and E

Explanation:

To verify which are solutions, substitute the given values into the left side of the equation and if equal to the right side then they are solutions.

A

2(20)² + 18(20) = 800 + 360 = 1160 ≠ 20 ← not a solution

B

2(1)² + 18(1) = 2 + 18 = 20 ← solution

C

2(- 2)² + 18(- 2) = 2(4) - 36 = 8 - 36 = - 28 ≠ 20 ← not a solution

D

Is a repeat of C

E

2(- 10)² + 18(- 10) = 2(100) - 180 = 200 - 180 = 20 ← solution

F

2(- 1)² + 18(- 1) = 2(1) - 18 = 2 - 18 = - 16 ≈ 20 ← not a solution

Then B and E are solutions to the equation

Answer 2

`\huge \mathrm{Answer࿐ }`

let's solve the quadratic equation :

• 
  `2 {x}^(2) + 18x = 20`

• 
  `2 {x}^(2) + 18x - 20 = 0`

• 
  `2 {x}^(2) + 20x -2 x - 20 = 0`

• 
  `2x(x + 10) - 2(x + 10) = 0`

• 
  `(2x - 2)(x + 10) = 0`

So, there are two cases :

Case - 1 (when, 2x - 2 = 0)

• 
  `2x - 2 = 0`

• 
  `2x = 2`

• 
  `x = 1`

Case - 2 (when, x + 10 = 0)

• 
  `x + 10 = 0`

• 
  `x = - 10`

Therefore the required options will be :

• B. 1 and E. -10