Complete the square to solve the following quadratic equation: x2+4x=41

Question

.(1 point)
Responses

x=2+35–√, 2−35–√
x equals 2 plus 3 Start Root 5 End Root comma 2 minus 3 Start Root 5 End Root

x=2+53–√, 2−53–√
x equals 2 plus 5 Start Root 3 End Root comma 2 minus 5 Start Root 3 End Root

x=−2+35–√, −2−35–√
x equals negative 2 plus 3 Start Root 5 End Root comma negative 2 minus 3 Start Root 5 End Root

x=−2+53–√, −2−53–√

Answer 1

x=2+3√5, 2−3√5

Answer 2

not the correct answer

Answer 3

Apologies for the incorrect response. Let's go through the steps again:

Step 1: Move the constant term to the right side of the equation:
x^2 + 4x - 41 = 0

Step 2: Take half of the coefficient of x and square it:
Half of 4 is 2, and 2 squared is 4.

Step 3: Add the squared number from Step 2 to both sides of the equation:
x^2 + 4x + 4 = 41 + 4
x^2 + 4x + 4 = 45

Step 4: Factor the left side of the equation as a perfect square:
(x + 2)^2 = 45

Step 5: Take the square root of both sides of the equation:
√[(x + 2)^2] = ±√45
(x + 2) = ±√45

Step 6: Solve for x by subtracting 2 from both sides of the equation:
x = -2 ± √45

The simplified solution is:
x = -2 ± √45

I apologize for any confusion caused.

Answer 4

that was not an option please give me an option

Answer 5

Apologies for misunderstanding your request. Let's try completing the square again:

Step 1: Move the constant term to the right side of the equation:
x^2 + 4x = 41

Step 2: Take half of the coefficient of x and square it:
Half of 4 is 2, and 2 squared is 4.

Step 3: Add the squared number from Step 2 to both sides of the equation:
x^2 + 4x + 4 = 41 + 4
(x + 2)^2 = 45

Step 4: Take the square root of both sides of the equation:
√[(x + 2)^2] = ±√45
x + 2 = ±√45

Step 5: Solve for x by subtracting 2 from both sides of the equation:
x = -2 ± √45

So the solutions to the quadratic equation x^2 + 4x = 41, after completing the square, are:
x = -2 ± √45

Answer 6

still not the answer

Answer 7

Apologies for the confusion. Let's try again:

Step 1: Move the constant term to the right side of the equation:
x^2 + 4x = 41

Step 2: Take half of the coefficient of x and square it:
Half of 4 is 2, and 2 squared is 4.

Step 3: Add the squared number from Step 2 to both sides of the equation:
x^2 + 4x + 4 = 41 + 4
(x + 2)^2 = 45

Step 4: Take the square root of both sides of the equation:
√[(x + 2)^2] = ±√45
x + 2 = ±√45

Step 5: Solve for x by subtracting 2 from both sides of the equation:
x = -2 ± √45

So the solutions to the quadratic equation x^2 + 4x = 41, after completing the square, are:
x = -2 ± √45

I apologize for any confusion caused.