The solution is x = 5 and x= -8
Step-by-step explanation:
Given equation is:
[tex]x^2=-3x+40[/tex]
Converting in standard form
[tex]x^2+3x-40 = 0[/tex]
The standard form of quadratic equation is:
[tex]ax^2+bx+c = 0[/tex]
Here
a = 1
b = 3
c = -40
Quadratic formula is given as:
[tex]x = \frac{-b+\sqrt{b^2-4ac}}{2a}\ \ \ \ , \ \ \ \ x = \frac{-b-\sqrt{b^2-4ac}}{2a}[/tex]
Putting the values of a, b and c
[tex]x = \frac{-3+\sqrt{(3)^2-4(1)(-40)}}{2(1)}\ \ \ \ , \ \ \ \ x = \frac{-3-\sqrt{(3)^2-4(1)(-40)}}{2(1)}\\x = \frac{-3+\sqrt{9+160}}{2}\ \ \ \ \ \ \ \ \ \ \ \ \ \ , \ \ \ \ x = \frac{-3-\sqrt{9+160}}{2}\\x = \frac{-3+\sqrt{169}}{2}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ , \ \ \ \ x = \frac{-3-\sqrt{169}}{2}\\x = \frac{-3+13}{2}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ , \ \ \ \ x = \frac{-3-13}{2}\\x = \frac{10}{2}\ \ \ \ \ \ \ \ \ \ \ \ \ , \ \ \ \ x = \frac{-16}{2}\\x = 5\ \ \ \ \ And \ \ \ \ \ \ x = -8[/tex]
Hence,
The solution is x = 5 and x= -8
Keywords: Quadratic equation, variables
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