Question:
The square of a number decreased by 3 times the number is 28 find all possible values for the number
Answer:
The possible values of number are 7 and -4
Solution:
Given that the square of a number decreased by 3 times the number is 28
To find: all possible values of number
Let "a" be the unknown number
From given information,
square of a number decreased by 3 times the number = 28
[tex]a^2 - 3a = 28[/tex]
[tex]a^2 - 3a - 28 = 0[/tex]
Let us solve the above quadratic equation
[tex]\text {For a quadratic equation } a x^{2}+b x+c=0, \text { where } a \neq 0[/tex]
[tex]x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]
Using the above formula,
[tex]\text { For } a^{2}-3 a-28=0 \text { we have } a=1, b=-3, c=-28[/tex]
[tex]\begin{aligned}&a=\frac{-(-3) \pm \sqrt{(-3)^{2}-4(1)(-28)}}{2 \times 1}\\\\&a=\frac{3 \pm \sqrt{9+112}}{2}\\\\&a=\frac{3 \pm \sqrt{121}}{2}=\frac{3 \pm 11}{2}\\\\&a=\frac{3+11}{2} \text { or } a=\frac{3-11}{2}\\\\&a=7 \text { or } a=-4\end{aligned}[/tex]
Thus the possible values of number are 7 and -4
