Question

Which x value makes this equation true? Explain how you can tell

2x^2 - x + 10 = 38
a) x=2
b) x=4
c) x=-4
d) x=6

Answer 1

The answer is b.

To find the value of x, we need to convert this into the form of a quadratic equation.

Subtract 38 from each side.

• 2x² - x + 10 - 38 = 38 - 38
• 2x² - x - 28 = 0

Solve by splitting the middle term.

• 2x² + 7x - 8x - 28 = 0
• x (2x + 7) - 4 (2x + 7) = 0
• x = 4, x = -7/2

Answer 2

b) x = 4

Step-by-step explanation:

`2x^2 - x + 10 = 38`

collect variables

`2x^2 - x + 10 - 38 = 0`

simplify

`2x^2 - x - 28 = 0`

breakdown

`2x^2 -8x + 7x - 28 = 0`

factor out

`2x(x - 4) + 7(x - 4) = 0`

collect into groups

`(2x + 7)(x - 4) = 0`

set to zero

`2x + 7 = 0, x - 4 = 0`

relocate variable

`2x = -7, x = 4`

final solutions

`x = -3.5, x = 4`