Question

The sum of a number and its square is 42. Which equation can be used to find the two numbers for which this is true?

x2 + x = 42
x2 + 2x = 42
x2 + x + 42 = 0
x2 + 2x + 42 = 0

Answer 1

The sum: "+"

a number: "x"

a square of a number: "x²"

Answer: x + x² = 42 → x² + x = 42

Answer 2

`x^(2)+x =42`

Explanation:

Let

x------> the number

we know that

The algebraic expression that represent the situation is equal to

`x^(2)+x =42` ----> quadratic equation

using a graphing tool-----> to resolve the quadratic equation

see the attached figure

The solutions are

`x=-7, x=6`

Verify each solution

For
`x=-7`

substitute in the expression

`x^(2)+x =42`

`(-7)^(2)+(-7) =42`

`49-7=42`

`42=42` -----> is true

For
`x=6`

substitute in the expression

`x^(2)+x =42`

`(6)^(2)+(6) =42`

`36+6=42`

`42=42` -----> is true