# The square of what number is 6 greater than 5 times the number

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The square of a number is 6 greater than 5 times the number. Let the number be denoted by X.

X^2 = 6 + 5X

=> X^2 - 5X - 6 = 0

=> X^2 - 6X + X - 6 = 0

=> X(X - 6) + 1(X - 6) = 0

=> (X + 1)(X - 6) = 0

=> X = -1 and X = 6

The square of the numbers -1 and 6 is 6 greater than 5 times the number.

givingiswinning | Student, Grade 10 | (Level 1) Valedictorian

Posted on

x^2 = 6 + 5x
x^2 - 5x - 6 = 0

multiply a by c and find the factors, and add up to b

X^2 - 6X + X - 6 = 0

group

(X^2 - 6X) +( X - 6)

factor

x (x - 6) + 1 ( x - 6)

(x + 1) (x - 6)

set equal to 0:
x + 1 =0

x = -1

x - 6 = 0

x = 6

atyourservice | Student, Grade 11 | (Level 3) Valedictorian

Posted on

The square of what number is 6 greater than 5 times the number

x^2 = 6 + 5x
now move the problems to the same side:

x^2 - 5x - 6 = 0

multiply a by c and find the factors, and add it to b

X^2 - 6X + X - 6 = 0

group

(X^2 - 6X) +( X - 6)

factor:

x (x - 6) + 1 ( x - 6)

(x + 1) (x - 6)

x = -1   x = 6