The sum of a number and its square is 72. Find the number.

The sum of a number, n, and its square n^2 is 72. In equation form, this is n + n^2 = 72. Try making this into a polynomial equaling 0. n + n^2 =72 subtract 72 n^2 + 1n -72 = 0 Now factor this polynomial (n-8) (n+9) = 0 Solutions to this problem are 8 and -9 Plug in for n to check. 8 + 64 = 72 8 is correct -9 + 81 = 72 -9 is also correct!!

Answered by Colleen1414 | 2024-06-10

The question asks us to find a number such that when it is added to its square, the result is 72. This can be expressed algebraically as x + x^2 = 72. To solve this, we need to rearrange the equation to one side to set it equal to zero: x^2 + x - 72 = 0.
Next, we factor the quadratic equation. The factors of -72 that add up to 1 are 8 and -9. Therefore, the factored equation is (x + 9)(x - 8) = 0.
Setting each factor equal to zero gives us x = -9 or x = 8. Since we are dealing with a real number, both of these solutions are valid. Hence, there are two numbers that satisfy the condition: -9 and 8.

Answered by EnverGjokaj | 2024-06-19

The number that satisfies the condition that the sum of a number and its square equals 72 can be found by solving the equation x + x 2 = 72 . This results in the factored equation ( x + 9 ) ( x − 8 ) = 0 , yielding solutions of x = 8 and x = − 9 . Therefore, the answers are 8 and -9.
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Answered by EnverGjokaj | 2024-12-26