When a number is added to its square the result is 90. find the number.

➷  We can form an equation:

x^2 + x = 90

Subtract 90 from both sides:

x^2 + x - 90 = 0

Now factorize:

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

Thus, x = 9 or x = -10

Either of these answers would work, but stick with 9 as your answer.

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ANSWER:  

When a number is added to its square the result is 90. The number is 9, -10

SOLUTION:

Let the number be "x"

Given, a number is added to it’s square.  This can be represented as,

number +  it’s square

Also given that, result is 90. Hence the above equation is equal to 90

we can solve this equation by factorizing the equation.

On rewriting the above equation, we get

Taking “x” as common, we get

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

(x + 10)(x – 9) = 0

x+10 = 0, x – 9 = 0

x = -10, 9

Hence, the values of x are 9, -10.