Solve the following quadratic equation by completing the square. (Enter your answers as a comma-separated list.)
a^2-12a+52=0
To solve the quadratic equation "a^2 - 12a + 52 = 0" by completing the square, follow these steps:
Step 1: Move the constant term to the other side of the equation:
a^2 - 12a = -52
Step 2: Take half of the coefficient of the linear term (12) and square it to find the value you need to add on both sides of the equation:
The half of 12 is 6, and squaring it gives 36.
Step 3: Add this squared value to both sides of the equation:
a^2 - 12a + 36 = -52 + 36
(a - 6)^2 = -16
Step 4: Rewrite the equation in perfect square form and isolate the square term:
(a - 6)^2 - (-16) = 0
(a - 6)^2 + 16 = 0
Step 5: Solve for a by taking the square root of both sides:
(a - 6) = ±√(-16)
The square root of a negative number is an imaginary number.
So, the solutions to the quadratic equation "a^2 - 12a + 52 = 0" using completing the square method are:
a = 6 ± 4i
Therefore, the comma-separated list of solutions is:
a = 6 + 4i, 6 - 4i