Respuesta :
Answer:
Quadratic formula: -5-√33/(under) 2 -5+√33/(under) 2
Using PQ formula: -5/2- √33/2 -5/2+ √33/2
Completing the square: - √33+5/2 √33-5/2
Numbers of real solutions: 2
Step-by-step explanation:
The solution of the given equations is [tex]x=\frac{-5+\sqrt{33}}{2},\:x=\frac{-5-\sqrt{33}}{2}[/tex]
We have given that,
x^2 + 5x = 2
We can write it as,
[tex]x^2+5x-2=0[/tex]
What is the quadratic formula?
[tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4\cdot \:a\cdot \left(c\right)}}{2\cdot \:a}[/tex]
[tex]x_{1,\:2}=\frac{-5\pm \sqrt{5^2-4\cdot \:1\cdot \left(-2\right)}}{2\cdot \:1}[/tex]
[tex]x_{1,\:2}=\frac{-5\pm \sqrt{33}}{2\cdot \:1}[/tex]
[tex]x_1=\frac{-5+\sqrt{33}}{2\cdot \:1},\:x_2=\frac{-5-\sqrt{33}}{2\cdot \:1}[/tex]
[tex]x=\frac{-5+\sqrt{33}}{2},\:x=\frac{-5-\sqrt{33}}{2}[/tex]
Therefore the solution of the given equations is [tex]x=\frac{-5+\sqrt{33}}{2},\:x=\frac{-5-\sqrt{33}}{2}[/tex].
To learn more about the quadratic equation visit:
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