Question

El cuadrado de un número menos 5 es igual a 220. ¿Cuál es ese número?

El cuadrado de un número mas el mismo número es igual a 306. ¿Cuál es ese número?

Answer 1

Answer: Im translating this to english, hope this is not a problem for you :)

"El cuadrado de un número menos 5 es igual a 220. ¿Cuál es ese número?"

This says that a number square subtracted by 5 is equal to 220:

n^2 - 5 = 220

now we need to isolate n:

n^2 = 225

n = √225 = 15

then our number is 15.

"El cuadrado de un número mas el mismo número es igual a 306. ¿Cuál es ese número?"

The sum betwen a squared number and the same number is equal to 306, and we want to find this number:

n^2 + n = 306

this is a cuadratic equation, here we can use Bhaskara:

n^2 + n - 306 = 0

if we have a equation of the form:

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

the solutions are:

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

in this case; a = 1, b= 1 and c = 306, we can replace this in the equation and get:

`n = ( -1 +/- √(1  +4*1*306) )/(2) = (-1 +/-√(1225) )/(2) = (1 +/- 35)/(2)`

So we have two solutions here; n = -36/2 = - 18 and n = 34/2 = 17

Answer 2

the question is English is

Part a) The square of a number minus 5 equals 220. What is that number?

Part b) The square of a number plus the same number equals 306. What is that number?

Part a) The square of a number minus 5 equals 220. What is that number?

Let

x--------> the number

we know that

`x^(2) -5= 220 \\ \\ x^(2)= 220+5 \\\\x^(2) =225 \\\\x=√(225) \\ \\x=15`

therefore

the answer Part 1) is

the number is 15

Part 2) The square of a number plus the same number equals 306. What is that number?

Let

x--------> the number

we know that

`x^(2) +x= 306`

using a graph tool------> to resolve the second order equation

see the attached figure

the solution are

x=-18

x=17

Check

for x=-18

`(-18)^(2) +(-18)= 306 \\ 306=306`

for x=17

`(17)^(2) +(17)= 306 \\ 306=306`

therefore

the answer Part 2) is

the numbers are -18 and 17

The answer in Spanish

Parte a)

Hagamos

x--------> el numero

Sabemos que

`x^(2) -5= 220 \\ \\ x^(2)= 220+5 \\\\x^(2) =225 \\\\x=√(225) \\ \\x=15`

por lo tanto

La respuesta de la parte 1) es

El numero es 15

Parte 2)

Hagamos

x--------> El numero

Sabemos que

`x^(2) +x= 306`

Usamos una herramienta grafica------> para resolver la ecuacion cuadratica

Ver la imagen adjunta

Las soluciones son

x=-18

x=17

Chequeamos

para x=-18

`(-18)^(2) +(-18)= 306 \\ 306=306`

para x=17

`(17)^(2) +(17)= 306 \\ 306=306`

por lo tanto

La respuesta de la parte 2) es

Los numeros son -18 and 17