If an integer is added to its square, the sum is 90. Find the integer with the help of quadratic equation.

Given:

If an integer is added to its square, the sum is 90.

 To do:

We have to find the integer with the help of quadratic equation.

Solution:

Let the integer be $x$.

This implies,

The square of the integer $x^2$.

According to the question,

$x+x^2=90$

$x^2+x-90=0$

Solving for $x$ by factorization method, we get,

$x^2+10x-9x-90=0$

$x(x+10)-9(x+10)=0$

$(x+10)(x-9)=0$

$x+10=0$ or $x-9=0$

$x=-10$ or $x=9$

Therefore, the values of the integers are $-10$ and $9$.

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Updated on: 10-Oct-2022

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