Answer:
the perfect squares are,
1. (x + 4)² - 10
2. (x + 6)² - 37
Explanation:
1.
x² + 8x + 6 = 0
the steps to make a perfect square are as follows:
1. move the constant to the right side of the equation,
x² + 8x = -6
2. take the half of the x term which in the given equation is 8,
8/2 = 4
3. square the half of the x term, 4² = 16
4. add the square to both sides of the equation,
x² + 8x + 16 = -6 + 16
the given equation is a perfect square now,
(x + 4)² = 10
(x + 4)² - 10
as we know that, (a + b)² = a² + b² + 2ab
(x + 4)² = x² + 16 + 8x which proves that our perfect square is right.
2.
x² + 12x - 1 = 0
let's follow the same steps again,
1. move the constant to the right side of the equation,
x² + 12x = 1
2. let's take half of x term which is 12,
12/2 = 6
3. let's square the half of the x term, 6² = 36
4. let's add the square of the half of the x term to both sides of equation,
x² + 12x + 36 = 1 + 36
the equation is a perfect square now,
(x + 6)² = 37
(x + 6)² - 37
as we know that, (x + 6)² = x² + 36 + 12x which verifies that our perfect square is right