Question

The sum of an integer and the square of the next consecutive integer is 29. Find the integer.

Answer 1

answer:4

Step-by-step explanation:

first choose a number whose next integer is minimal to 29

we gat to know that the integer is 5 whose squre is 25

now add the privious integer

4+squre of 5

4+25=29

Answer 2

Step-by-step explanation:

$Let \: x \: to \: be \: the \: integer. \\ \bold\blue{According \: to \: question,} \\ \\ \implies x + {(x + 1)}^{2} = 29 \\ \implies x + ( {x}^{2} + 2x + 1) = 29 \\ \implies {x}^{2} + 3x + 1 = 29 \\ \implies {x}^{2} + 3x + 1 - 29 = 0 \\ \implies {x}^{2} + 3x - 28 = 0 \\ \implies {x}^{2} + 7x - 4x - 28 = 0 \\ \implies x(x + 7) - 4(x + 7) = 0 \\ \implies \boxed{(x - 4)(x + 7) = 0} \\ \\ \\ \\ \\ \bold {Therefore} \: \: \: \: \: \: \boxed{ x \: = 4 \:, - 7}$

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