If the sum of a number and its square is 182, | vedclass

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Question

(D) Let the number be $x$.According to the problem,the sum of the number and its square is $182$.So,$x^2 + x = 182$.Rearranging the equation,we get $x

Vedclass · Accepted Answer

$13$

Vedclass · Answer

(D) Let the number be $x$.According to the problem,the sum of the number and its square is $182$.So,$x^2 + x = 182$.Rearranging the equation,we get $x^2 + x - 182 = 0$.To solve this quadratic equation,we look for two numbers whose product is $-182$ and whose sum is $1$.These numbers are $14$ and $-13$.So,$x^2 + 14x - 13x - 182 = 0$.$x(x + 14) - 13(x + 14) = 0$.$(x - 13)(x + 14) = 0$.This gives $x = 13$ or $x = -14$.Since $13$ is one of the options,the correct number is $13$.

If the sum of a number and its square is $182$,what is the number?

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