Solve the quadratic equation x2+8x−30=0 by completing the square.
What are the solutions to the quadratic equation, if any?

x=4±46−−√
This equation has no real solutions.
x=4±34−−√
x=±46−−√

Answer:

               [tex]\bold{x=-4\pm\sqrt{46}}[/tex]

Step-by-step explanation:

[tex](a+b)^2=a^2+2ab+b^2\\\\\\x^2+8x-30=0\\\\\underbrace{x^2+2\cdot x\cdot 4+4^2}-4^2-30=0\\\\{}\qquad(x+4)^2\,-\,16-30=0\\\\{}\qquad\ \ (x+4)^2=46\\\\ {}\qquad\ \ x+4=\pm\sqrt{46}\\\\ {}\qquad\ \ x=-4\pm\sqrt{46}[/tex]

The solution to the quadratic equation by completing the square will be

x = -4 ± √46. The correct option is A.

It is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The given equation will be solved as below:-

x² + 8x − 30 = 0

Completing the square for the above equation.

( x + 4 )² - 16 - 30 = 0

( x + 4 )² = 46

x + 4 = ±√46

x = ±√46 - 4

Therefore, the solution to the quadratic equation by completing the square will be x = -4 ± √46. The correct option is A.

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Voici un programme de calcul :
Choisir un nombre
Multiplier ce nombre par 4
Ajouter 8
Multiplier le résultat par 2
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Dans la suite de l'exercice, on nomme x le nombre choisi au départ.
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On pose B = (4 + x)2 – x2
Prouver que les expressions A et B sont égales pour toutes les valeurs de x.
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On rappelle que les réponses doivent être justifiées.
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