Solve each of the following quadratic equations by completing the square.
Problem#22 sect. 10.2
x^2-6x-3=0
My answer I keep getting two different answers : I get these two everytime i do it differently.
I get : x= 3 +- radical(12) or x = 3+-2radical(3)
Problem #28 sect10.2
2x^2+10x+11=0
My answer i keepgetting two different answer i don't know which one is correct:
x = (-10+-radical(12))/(2(2))
or
x=-2.5+-0.5radical(3)
To solve each of these quadratic equations by completing the square, follow these steps:
Step 1: Move the constant term to the other side of the equation.
Step 2: Complete the square by adding the square of half the coefficient of the x term.
Step 3: Rewrite the equation as a perfect square trinomial.
Step 4: Solve the quadratic equation by taking the square root of both sides.
Step 5: Simplify and solve for x.
Let's solve each problem:
Problem #22: x^2 - 6x - 3 = 0
Step 1: Move the constant term to the other side.
x^2 - 6x = 3
Step 2: Complete the square. Half of the coefficient of the x term is -6/2 = -3. Square that to get 9 and add it to both sides.
x^2 - 6x + 9 = 3 + 9
x^2 - 6x + 9 = 12
Step 3: Rewrite the equation as a perfect square trinomial.
(x - 3)^2 = 12
Step 4: Solve the quadratic equation by taking the square root of both sides.
x - 3 = ±√12
Step 5: Simplify and solve for x.
x = 3 ± √12
x = 3 ± 2√3
So the solutions to the equation x^2 - 6x - 3 = 0 are x = 3 ± √12 or x = 3 ± 2√3.
Problem #28: 2x^2 + 10x + 11 = 0
Step 1: Move the constant term to the other side.
2x^2 + 10x = -11
Step 2: Complete the square. Half of the coefficient of the x term is 10/2 = 5. Square that to get 25 and add it to both sides.
2x^2 + 10x + 25 = -11 + 25
2x^2 + 10x + 25 = 14
Step 3: Rewrite the equation as a perfect square trinomial.
2(x + 5)^2 = 14
Step 4: Solve the quadratic equation by taking the square root of both sides.
x + 5 = ±√(14/2)
Step 5: Simplify and solve for x.
x + 5 = ±√7
x = -5 ± √7
So the solutions to the equation 2x^2 + 10x + 11 = 0 are x = -5 ± √7.