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=0
you multiply all of it by -1 to change the x into postive.
therefore,
x^2+7x-11=0
then apply this to the fo9rmula
-b+- the sqaure root of (b^2 - 4*a*c)/2a
where a = 1
b=7
c=-11
work out the answer, its very easy (:
To solve the quadratic equation -x^2 - 7x = -11 by completing the square, follow these steps:
Step 1: Move the constant term to the other side of the equation
Start by adding 11 to both sides of the equation to eliminate the constant term on the right side:
-x^2 - 7x + 11 = 0
Step 2: Group the x terms
Rearrange the equation to group the x terms together:
(-x^2 - 7x) + 11 = 0
Step 3: Factor out the coefficient of the x^2 term
Factor out -1 from the x terms:
-(x^2 + 7x) + 11 = 0
Step 4: Complete the square
Take half of the coefficient of the x term (in this case, half of 7 is 7/2) and square it (49/4). Add this value inside the parentheses, and also subtract it outside the parentheses to keep the equation balanced:
-(x^2 + 7x + 49/4 - 49/4) + 11 = 0
Step 5: Simplify the equation
Simplify the equation inside the parentheses:
-(x^2 + 7x + 49/4 - 49/4) + 11 = 0
-(x^2 + 7x + 49/4) + 49/4 + 11 = 0
-(x + 7/2)^2 + 49/4 + 44/4 = 0
-(x + 7/2)^2 + 93/4 = 0
Step 6: Solve for x
To solve for x, isolate the squared term:
-(x + 7/2)^2 = -93/4
Step 7: Take the square root of both sides
Take the square root of both sides of the equation to eliminate the square and solve for x:
x + 7/2 = ±√(-93/4)
Step 8: Simplify the radicals
Simplify the radicals on the right side of the equation:
x + 7/2 = ±√(-93)/2
x + 7/2 = ±(√93/2)i
Step 9: Solve for x
To solve for x, isolate x by subtracting 7/2 from both sides:
x = -7/2 ± (√93/2)i
The solution to the quadratic equation -x^2 - 7x = -11, expressed in simplest radical form, is:
x = -7/2 ± (√93/2)i