Respuesta :

CHERLYNnotCHERRY

Answer:

Since the input values are -7/2 and 2. So the answer is C.

Step-by-step explanation:

Given that when x-value is substituted into the function, you get 19. So in order to find the input value (x), you have to make the function equals 19 :

[tex]f(x) = 2 {x}^{2} + 3x + 5[/tex]

[tex]let \: f(x) = 19[/tex]

[tex]2 {x}^{2} + 3x + 5 = 19[/tex]

Next, you have to factorize it :

[tex]2 {x}^{2} + 3x + 5 - 19 = 0[/tex]

[tex]2 {x}^{2} + 3x - 14 = 0[/tex]

[tex]2 {x}^{2} + 7x - 4x - 14 = 0[/tex]

[tex]x(2x + 7) - 2(2x + 7) = 0[/tex]

[tex](x - 2)(2x + 7) = 0[/tex]

Lastly, solve it :

[tex]x - 2 = 0[/tex]

[tex]x = 2[/tex]

[tex]2x + 7 = 0[/tex]

[tex]x = - \frac{7}{2} [/tex]

Answer:

C. 2

Step-by-step explanation:

1. Set up the equation

19 = 2x² + 3x + 5 → 2x² + 3x = 14

Divide by two to get a=1

x² + 1.5x = 7

2. Complete the square using (b/2)²

(1.5/2)² = 0.5625

x² + 1.5x + 0.5625 = 7 + 0.5625

3. Factor perfect square trinomial and simplify

√x² + 1.5x + √0.5625 = 7 + 0.5625

(x + 0.75)² = 7.5625

4. Square root each side

√(x + 0.75)² = √7.5625

x + 0.75 = ±2.75

5. Set up two possibilities and solve

x = -0.75 ± 2.75

x = -0.75 + 2.75 = 2

x = -0.75 - 2.75 = -3.5

6. Plug in the values

2(2)² + 3(2) + 5 = 19

2(-3.5)² + 3(-3.5) + 5 = -30

x = 2