Question

Find a positive real number such that its square is equal to 15 times the number increased by 286

Answer 1

The positive real number is 26

Explanation:

Let

x ----> the number

we know that

The algebraic expression that represent this problem is

`x^(2) =15x+286`

so

`x^(2)-15x-286=0`

The formula to solve a quadratic equation of the form

`ax^(2) +bx+c=0`

is equal to

`x=\frac{-b(+/-)\sqrt{b^(2)-4ac}} {2a}`

in this problem we have

`x^(2)-15x-286=0`

so

`a=1\\b=-15\\c=-286`

substitute in the formula

`x=\frac{-(-15)(+/-)\sqrt{-15^(2)-4(1)(-286)}} {2(1)}`

`x=\frac{15(+/-)√(1,369)} {2}`

`x=(15(+/-)37)/(2)`

`x_1=(15(+)37)/(2)=26`

`x_2=(15(-)37)/(2)=-11` ---> the solution cannot be negative

therefore

The positive real number is 26