solve the following quadratic equation doing the perfect square trinomial pattern: X^2 - 16x + 64
To solve the equation x^2 - 16x + 64 using the perfect square trinomial pattern, we need to follow these steps:
Step 1: Identify the coefficients a, b, and c in the equation.
In this case, a = 1, b = -16, and c = 64.
Step 2: Divide the coefficient of x by 2 and square the result.
Taking half of -16, we get (-16/2)^2 = (-8)^2 = 64.
Step 3: Rewrite the equation by adding and subtracting the result from step 2 inside the parentheses.
x^2 - 16x + 64 can be rewritten as x^2 - 16x + 64 + 64 - 64.
Step 4: Group the first three terms and the last two terms separately.
(x^2 - 16x + 64) + (64 - 64).
Step 5: Factor the perfect square trinomial in the first parentheses.
(x - 8)^2 + (64 - 64).
Step 6: Simplify the equation.
(x - 8)^2 + 0.
Step 7: Obtain the simplified form of the equation.
(x - 8)^2 = 0.
Step 8: Take the square root of both sides.
√[(x - 8)^2] = √0.
Step 9: Remove the square root by setting x - 8 equal to 0 and solve for x.
x - 8 = 0.
Step 10: Add 8 to both sides.
x = 8.
Therefore, the solution to the quadratic equation x^2 - 16x + 64 = 0 using the perfect square trinomial pattern is x = 8.