What are the solutions of x2 = 8 - 5x? - 를 들 는 01-17

3 answers
Question:

What are the solutions of x2 = 8 - 5x?
- 를 들

01-17

Answers

Given: The equation [tex]x^2=8-5x[/tex]

we can write this as;

[tex]x^2+5x-8=0[/tex]

The general equation of quadratic formula for [tex]ax^2+bx+c=0[/tex] where a, b and c are constant ;

then the solution for this equation  is given by;

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

From the given equation;

we have a =1 , b =5 and c=-8

then, the solution of the given equation is;

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}=\frac{-5\pm\sqrt{5^2-4(1)(-8)}}{2(1)}[/tex]

or

[tex]x=\frac{-5\pm\sqrt{25+32}}{2}=\frac{-5\pm\sqrt{57}}{2}[/tex]

therefore, the solution of the given equation is;

[tex]x=\frac{-5+\sqrt{57}}{2}[/tex] and [tex]x=\frac{-5-\sqrt{57}}{2}[/tex]

That can be re-written:

x^2 + 5x -8 = 0

We use the Quadratic Formula

a=1

b = 5

c = -8

x = [-b +- sq root (b^2 - 4ac) ] / 2a

x = [-5 +- sq root (25 - - 32)] / 2

x1 = [-5 + sq root (57)] / 2

x1 = 1.27491722

x2 = [-5 - sq root (57)] / 2

x2 = -6.2749172176

Step-by-step explanation:

X=1 because 8-5=3so the x has to equal 1

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