Answer:
As exact answers:
[tex]x=\frac{-5-\sqrt{57} }{2}[/tex] and [tex]x=\frac{-5+\sqrt{57} }{2}[/tex]
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
[tex]x=\frac{-b±\sqrt{b^{2}-4ac} }{2a}[/tex] (Ignore the Â, it's a formatting error)
[tex]x=\frac{-5±\sqrt{5^{2}-4(1)(-8)} }{2(1)}[/tex] Simplify
[tex]x=\frac{-5±\sqrt{25-(-32)} }{2}[/tex] Two negatives make a positive
[tex]x=\frac{-5±\sqrt{57} }{2}[/tex]
Split the equation at the ± for plus and minus:
[tex]x=\frac{-5+\sqrt{57} }{2}[/tex] = 1.27491722 ≈ 1.3
[tex]x=\frac{-5-\sqrt{57} }{2}[/tex] = -6.2749172 ≈ -6.3
Therefore the solutions are 1.3 and -6.3.
