Respuesta :
p^2 + 4p = 1
(p + 2)^2 - 4 = 1
(p+2)^2 = 1 + 4 = 5
p+2 = +/- sqrt5
p = +/- sqrt5 - 2 Answer
(p + 2)^2 - 4 = 1
(p+2)^2 = 1 + 4 = 5
p+2 = +/- sqrt5
p = +/- sqrt5 - 2 Answer
The solutions to the equation [tex]p^2+4p=1[/tex] using completing the square method are [tex]-2- \sqrt{5}[/tex] and [tex]-2+ \sqrt{5}[/tex]
The given equation is:
[tex]p^2+4p=1[/tex]
Add [tex](\frac{4}{2})^2[/tex] to both sides of the equation
[tex]p^2+4p+(\frac{4}{2})^2= 1 + (\frac{4}{2})^2\\\\p^2+4p+2^2=1+2^2\\\\(p+2)^2=1+4\\\\(p+2)^2=5\\\\[/tex]
Find the square root of both sides
[tex]p+2 = \pm\sqrt{5}\\\\p=-2\pm sqrt{5} \\\\p = -2 - sqrt{5}\\\\p=-2+ \sqrt{5}[/tex]
The roots of the equation are [tex]-2- \sqrt{5}[/tex] and [tex]-2+ \sqrt{5}[/tex]
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