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

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

$x^{2} -5= 220 \\ \\ x^{2}= 220+5 \\\\x^{2} =225 \\\\x=\sqrt{225} \\ \\x=15$

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

$x^{2} -5= 220 \\ \\ x^{2}= 220+5 \\\\x^{2} =225 \\\\x=\sqrt{225} \\ \\x=15$

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

Answer 2

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:

$n = \frac{ -1 +/- \sqrt{1  +4*1*306} }{2} = \frac{-1 +/-\sqrt{1225} }{2} = \frac{1 +/- 35}{2}$

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