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?

Answer 1

Answer:

$x^{2}+x =42$

Step-by-step 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

Answer 2

The sum: "+"

a number: "x"

a square of a number: "x²"

Answer: x + x² = 42 → x² + x = 42