Solution: The first term 2x² can't be changed to a complete square form. If we want to change it to the complete square form, we need to change 2x² to 4x². So, multiply both sides of the equation by 2 2x² + 8x - 12 = 0 ------------------------- multiplied by 2 4x² + 16x - 24 = 0
then change it to complete quadratic form by adding 16 to both sides 4x² + 16x - 24 = 0 4x² + 16x + 16 - 24 = 16 4x² + 16x + 16 = 16 + 24 4x² + 16x + 16 = 40 (2x + 4)(2x + 4) = 40 (2x + 4)² = 40 This is the complete quadratic form of the equation.
Because there is no option of the solution, we can modify the equation by multiplying the two sides by a square number. I multiply the equation by 4. (2x + 4)² = 40 4 (2x + 4)² = 4 × 40 4 (2x + 4)² = 160 4 (2x + 4)(2x + 4) = 160 2(2x + 4) 2(2x + 4) = 160 (4x + 8)(4x + 8) = 160 (4x + 8)² = 160
