complete the square(real or imaginary)
a^2-12a+35=0
my answers are
a=7
a=5
you are correct
7,5 r right
To complete the square for the quadratic equation a^2 - 12a + 35 = 0, we follow these steps:
Step 1: Move the constant term (35) to the other side of the equation:
a^2 - 12a = -35
Step 2: To complete the square, take half of the coefficient of the 'a' term (-12), and square it. Half of -12 is -6, and -6 squared is 36. Add this value to both sides of the equation:
a^2 - 12a + 36 = -35 + 36
a^2 - 12a + 36 = 1
Step 3: Rewrite the left side of the equation as a perfect square trinomial:
(a - 6)^2 = 1
Step 4: Take the square root of both sides to solve for 'a':
√(a - 6)^2 = ±√1
(a - 6) = ±1
Step 5: Solve for 'a' by isolating it:
For a + 6 = 1:
a = 1 - 6
a = -5
For a + 6 = -1:
a = -1 - 6
a = -7
So, the solutions are:
a = -5 and a = -7