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12 added to the square of a number is equal to 11 times the number,
minus 18. What is the number? (There are two solutions.)
a. 12 + x = 11x − 18, 3 or 5 c. 7 + x2 = 7x − 5, 4 or 5
b. 7 + x2 = 7x − 5, 6 or 7 d. 12 + x2 = 11x − 18, 5 or 6

Answer :

Onoriodefelix

Answer:

d. 12 + x^2 = 11x - 18, 5 or 6

Step-by-step explanation:

Let the number be x

12 + x^2 = 11x - 18

Rearrange the equation

x^2 + 12 - 11x + 18 = 0

x^2 - 11x + 12 + 18 = 0

x^2 - 11x + 30 = 0

Factorise

(x - 5)(x - 6) = 0

x - 5 = 0 Or x - 6 = 0

x = 5 Or x = 6

Answer:

d) [tex]x^2+12=11x-18[/tex],  [tex]x=5[/tex] or [tex]x=6[/tex]

Step-by-step explanation:

Let the number be '[tex]x[/tex]'.

According to the given statement, the equation is:

[tex]x^2+12=11x-18[/tex]

Solving the equation:

          [tex]x^2-11x+12+18=0\\x^2-11x+30=0\\[/tex]

Factorizing the equation for the value of '[tex]x[/tex]'

         [tex]x^2-6x-5x+30=0\\x(x-6)-5(x-6)=0\\[/tex]

Taking common from the equation to make the factors of the equation and equating it to zero.

                [tex](x-5)(x-6)=0\\\\(x-5)=0, (x-6)=0\\\\x=5 \\Or \\x=6[/tex]

x=5 Or x=6

       

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