Answer:
x = sqrt(10) - 9 or x = -9 - sqrt(10)
Step-by-step explanation by completing the square:
Solve for x:
x^2 + 18 x + 71 = 0
Subtract 71 from both sides:
x^2 + 18 x = -71
Add 81 to both sides:
x^2 + 18 x + 81 = 10
Write the left hand side as a square:
(x + 9)^2 = 10
Take the square root of both sides:
x + 9 = sqrt(10) or x + 9 = -sqrt(10)
Subtract 9 from both sides:
x = sqrt(10) - 9 or x + 9 = -sqrt(10)
Subtract 9 from both sides:
Answer: x = sqrt(10) - 9 or x = -9 - sqrt(10)
The solution of the provided quadratic equation obtained with the help of completing the square method is x=-9±√10.
A quadratic equation is the equation in which the unknown variable is one and the highest power of the unknown variable is two.
The standard form of the quadratic equation is,
[tex]ax^2+bx+c=0[/tex]
Here,(a,b, c) is the real numbers and (x) is the variable.
The given quadratic equation is,
[tex]x^2+18x+71 = 0[/tex]
Solve it further with the help of competing the square method using the following formula,
[tex]a(x+d)^2+e=0[/tex]
Here, d=b/2a and e=c-b²/4a.
Thus, the value of d is
[tex]d=\dfrac{18}{2\times1}\\d=9[/tex]
The value of e is
[tex]e=71-\dfrac{18^2}{4\times1}\\e=-10[/tex]
Put the value in the above formula as,
[tex](x+9)^2+-10=0\\x+9=\pm \sqrt{10}\\x=-9\pm \sqrt{10}[/tex]
Hence, the solution of the provided quadratic equation obtained with the help of completing the square method is x=-9±√10.
Learn more about the quadratic equation here;
https://brainly.com/question/1214333
