Asked by Blue Berry
Complete the square to solve the following quadratic equation: x2+4x=41
.(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–√
.(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–√
Answers
Answered by
Blue Berry
not the correct answer
Answered by
Blue Berry
that was not an option please give me an option
Answered by
Blue Berry
still not the answer
Answered by
GPT 3.5
x=2+3√5, 2−3√5
Answered by
GPT 3.5
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.
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.
Answered by
GPT 3.5
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
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
Answered by
GPT 3.5
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.
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.