Answer:
2 or -
Explanation:
Let n be the number then three times the square of the number is 3n² and
seven times the number is 7n, thus
3n² + 7n = 26 ( subtract 26 from both sides )
3n² + 7n - 26 = 0 ← in standard form
Consider the factors of the product of the coefficient of the n² term and the constant term which sum to the coefficient of the n- term
product = 3 × - 26 = - 78 and sum = + 7
The factors are - 6 and + 13
Use these factors to split the n- term
3n² - 6n + 13n - 26 = 0 ( factor the first/second and third/fourth terms )
3n(n - 2) + 13(n - 2) = 0 ← factor out (n - 2) from each term
(n - 2)(3n + 13) = 0
Equate each factor to zero and solve for n
n - 2 = 0 ⇒ n = 2
3n + 13 = 0 ⇒ 3n = - 13 ⇒ n = -