Ten times an integer is added to seven times it's square. If the result is 152, what was the original number?

Required number is 4.

Step-by-step explanation:

Let the required number be a.

Given,

Sum of ten times the integer and seven times it's square is 152.

= > Ten times of a + seven times of it's square = 152

= > 10 (a) + 7 (a) ^2 = 152

= > 10a + 7a^2 - 152 = 0

= > 7a^2 + 10a - 152 = 0

= > 7a^2 + (38 - 28) a - 152 = 0

= > 7a^2 + 38a - 28a - 152 = 0

= > a (7a + 38) - 4 (7a + 38) = 0

= > (a - 4) (7a + 38) = 0

= > a = 4 or - 38 / 7

Hence the required number is 4.