Respuesta :
When 6 is subtracted from the square of a number, the result is 5 times the number, then the negative solution is -1
Solution:
Given that when 6 is subtracted from the square of a number, the result is 5 times the number
To find: negative solution
Let "a" be the unknown number
Let us analyse the given sentence
square of a number = [tex]a^2[/tex]
6 is subtracted from the square of a number = [tex]a^2 - 6[/tex]
5 times the number = [tex]5 \times a[/tex]
So we can frame a equation as:
6 is subtracted from the square of a number = 5 times the number
[tex]a^2 - 6 = 5 \times a\\\\a^2 -6 -5a = 0\\\\a^2 -5a -6 = 0[/tex]
Let us solve the above quadratic equation
For a quadratic equation [tex]ax^2 + bx + c = 0[/tex] where [tex]a \neq 0[/tex]
[tex]x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]
Here in this problem,
[tex]a^2-5 a-6=0 \text { we have } a=1 \text { and } b=-5 \text { and } c=-6[/tex]
Substituting the values in above quadratic formula, we get
[tex]\begin{array}{l}{a=\frac{-(-5) \pm \sqrt{(-5)^{2}-4(1)(-6)}}{2 \times 1}} \\\\ {a=\frac{5 \pm \sqrt{25+16}}{2}=\frac{5 \pm \sqrt{49}}{2}} \\\\ {a=\frac{5 \pm 7}{2}}\end{array}[/tex]
We have two solutions for "a"
[tex]\begin{array}{l}{a=\frac{5+7}{2} \text { and } a=\frac{5-7}{2}} \\\\ {a=\frac{12}{2} \text { and } a=\frac{-2}{2}}\end{array}[/tex]
a = 6 or a = -1
We have asked negative solution. So a = -1
Thus the negative solution is -1
