Question

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

Answer 1

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➷  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 2

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

$x+x^{2}$

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

$\begin{array}{l}{x+x^{2}=90} \\ {x^{2}+x-90=0}\end{array}$

we can solve this equation by factorizing the equation.

$x^{2}+1 \times x-9 \times 10=0$

On rewriting the above equation, we get

$\begin{array}{l}{x^{2}+(10-9) \times x-9 \times 10=0} \\ {x^{2}+10 x-9 x-9 \times 10=0}\end{array}$

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.