Complete the square to Solve Quadratic Equation:
Solve the equation. Express the answer in simplest radical form.
-x^2-7x=-11
Please Help!!!! Thanks.
-x^2-7x=-11
x^2 - 7x = 11
x^2 - 7x + 49/4 = 11 + 49/4
(x - 7/2)^2 = 44/4 + 49/4
x - 7/2 = ± √93/2
x = (7 ±√93)/2
Thank you so much, but I was wondering:
-x^2-7x=-11
x^2 - 7x = 11
You have to divide by -1, wouldn't it be positive 7x.
YOU ARE RIGHT!
good for you for catching that.
I am sure you can make the necessary changes.
(there is one small change)
This is not a trigonometry question.
x^2 + 7x + (7/2)^2 = 11 + (7/2)^2
(x + 7/2)^2 = 23 1/4
x = -7/2 +/- sqrt(93)/2
Thank you so much!!!!
Could you please help me with another type of trig math question. I greatly appreciate your help.
To solve the quadratic equation -x^2-7x=-11 by completing the square, follow these steps:
Step 1: Move the constant term to the right side of the equation:
-x^2 - 7x = -11
Add 11 to both sides of the equation:
-x^2 - 7x + 11 = 0
Step 2: Divide the coefficient of the x term by 2 and square it. Add this result to both sides of the equation. This step is essential for completing the square.
In this case, the coefficient of the x term is -7.
(-7/2)^2 = 49/4
Add 49/4 to both sides of the equation:
-x^2 - 7x + 49/4 + 11 = 49/4
Simplifying the right side:
-x^2 - 7x + 49/4 + 44/4 = 49/4
-x^2 - 7x + 93/4 = 49/4
Step 3: Rewrite the left side of the equation as a squared binomial. This step completes the square.
(x - a)^2 = x^2 - 2ax + a^2
For our equation, the squared binomial will look like (x + b)^2.
To find 'b', we take half of the coefficient of the x-term (-7/2). In this case, b is -7/2.
(x - 7/2)^2 = x^2 - 2(x)(-7/2) + (7/2)^2
(x - 7/2)^2 = x^2 + 7x + 49/4
Step 4: Rewrite the equation with the completed square and simplify the right side:
(x - 7/2)^2 = 49/4 - 93/4
(x - 7/2)^2 = -44/4
(x - 7/2)^2 = -11
Step 5: Take the square root of both sides of the equation:
√((x - 7/2)^2) = ±√(-11)
Step 6: Solve for x by isolating it:
x - 7/2 = ±i√11
x = 7/2 ± i√11
So the solutions to the quadratic equation -x^2 - 7x = -11, expressed in simplest radical form, are:
x = 7/2 + i√11
x = 7/2 - i√11