Use the method of completing the square to transform the quadratic equation into the equation form (x – p)2 = q. 12 - 8x2 + x4 = 0 a) (x2 - 4)2 = -4 b) (x2 - 4)2 = 4 c) (x2 - 2)2 = -4 d) (x2 - 2)2 = 4its b

Incorrect

(x + 2)2 = 8

Move the constant term to the right:

-4 + 4x + x2 = 0

-4 + 4x + 4 + x2 = 0 + 4

Reorder and combine:

-4 + 4 + 4x + x2 = 0 + 4

0 + 4x + x2 = 0 + 4

4x + x2 = 0 + 4

4x + x2 = 4

The x term is 4x. Take half its coefficient 2. Square it and add 4 to both sides.

4x + 4 + x2 = 4 + 4

Reorder and combine the terms:

4 + 4x + x2 = 4 + 4

4 + 4x + x2 = 8

Factor a perfect square:

(x + 2)2 = 8

if triangle abc is congruent to triangle def, their interior angles are congruent, because congruent parts of congruent triangles are congruent (cpctc).

that means ∠d is congruent to ∠a; ∠d is equal to 8x - 2.

interior angles of all triangles add to equal 180 degrees, so you can set the sum of these interior angle values equal to 180 and solve for x.

180 = (8x - 2) + 22 + 72

180 = 8x - 2 + 22 + 72

180 = 8x + 92

88 = 8x

11 = x

x = 11