Question

Which are the solutions of x2 = –5x + 8?

Answer 1

Answer:

As exact answers:

$x=\frac{-5-\sqrt{57} }{2}$  and  $x=\frac{-5+\sqrt{57} }{2}$

As decimal answers:

x = -6.2749172 ≈-6.3

x = 1.27491722 ≈  1.3

Step-by-step explanation:

For quadratic equations, you can use the quadratic formula. Rearrange the equation to standard from, which is ax² + bx + c = 0.

x² = –5x + 8

x² + 5x - 8 = 0

State the values for "a", "b" and "c",

a = 1; b = 5; c = -8

$x=\frac{-b±\sqrt{b^{2}-4ac} }{2a}$            (Ignore the Â, it's a formatting error)

$x=\frac{-5±\sqrt{5^{2}-4(1)(-8)} }{2(1)}$           Simplify

$x=\frac{-5±\sqrt{25-(-32)} }{2}$               Two negatives make a positive

$x=\frac{-5±\sqrt{57} }{2}$  

Split the equation at the ± for plus and minus:

$x=\frac{-5+\sqrt{57} }{2}$  = 1.27491722 ≈ 1.3

$x=\frac{-5-\sqrt{57} }{2}$  = -6.2749172 ≈ -6.3

Therefore the solutions are 1.3 and -6.3.