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–√
x=2+3√5, 2−3√5
To solve the quadratic equation x^2 + 4x = 41 by completing the square, follow these steps:
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)(x + 2) = 45
Step 5: Simplify the equation:
(x + 2)^2 = 45
Step 6: Take the square root of both sides of the equation:
√[(x + 2)^2] = ±√45
(x + 2) = ±√45
Step 7: 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 and x = -2 - √45
not the correct answer
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.
that was not an option please give me an option
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
still not the answer
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.