Question

What are the exact solutions of x2 = 5x + 2? (1 point)

Answer 1

Answer:

First one:

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

Step-by-step explanation:

x² = 5x + 2

x² - 5x - 2 = 0

Using quadratic formula:

x = [-(-5) +/- sqrt[(-5)² - 4(1)(-2)]/2(1)

x = [5 +/- sqrt(33)]/2

Answer 2

Answer:

A. x equals 5 plus or minus the square root of thirty-three all over 2

Step-by-step explanation:

Let's move all the terms to one side:

$x^2=5x+2$

$x^2-5x-2=0$

Now, we want to use the quadratic formula, which states that for a quadratic equation of the form $ax^2+bx+c=0$, the roots can be found with the equation: $x=\frac{-b+\sqrt{b^2-4ac} }{2a}$ or $x=\frac{-b-\sqrt{b^2-4ac} }{2a}$.

Here, a = 1, b = -5, and c = -2, so plug these in:

$x=\frac{-(-5)+\sqrt{(-5)^2-4(1)(-2)} }{2(1)}=x=\frac{5+\sqrt{25+8} }{2}=\frac{5+\sqrt{33} }{2}$

OR

$x=\frac{-(-5)-\sqrt{(-5)^2-4(1)(-2)} }{2(1)}=x=\frac{5-\sqrt{25+8} }{2}=\frac{5-\sqrt{33} }{2}$

Thus, the answer is A.

Hope this helps!