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What are the exact solutions of x2 = 5x + 2?

x = x equals 5 plus or minus the square root of thirty-three all over 2
x = x equals negative 5 plus or minus the square root of thirty-three all over 2
x = x equals 5 plus or minus the square root of seventeen all over 2
x = x equals negative 5 plus or minus the square root of seventeen all over 2

Respuesta :

wolf1728
x^2 = 5x + 2
x^2 -5x -2 = 0
a = 1
b= -5
c= -2

x = [-b +- sq root (b^2 -4 ac)] / 2a
x = [--5 +- sq root (25 --8)] / 2a
x = [ 5 +- sq root (33)] / 2

Answer is "a"
boffeemadrid

Answer:

Step-by-step explanation:

The given equation is:

[tex]x^2=5x+2[/tex]

which can be rewritten as:

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

Now, since it is a quadratic equation, thus by using the discriminant method, we have

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

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

[tex]x=\frac{5{\pm}\sqrt{25+8}}{2}[/tex]

[tex]x=\frac{5{\pm}\sqrt{33}}{2}[/tex]

Thus, the value of x is equal to 5 plus or minus the square root of thirty-three all over 2, therefore option (A) is correct.

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