The question is: Which equation has the same solution as x² + 8x – 33 = 0?
The answer choices are:
- (1) (x + 4)² = 49
- (2) (x – 4)² = 49
- (3) (x + 4)² = 17
- (4) (x – 4)² = 17
Expanding option (2):
(x – 4)² = 49 ⟶ (x – 4)(x – 4) = 49 ⟶ x² – 8x + 16 = 49 ⟶ x² – 8x – 33 = 0
This matches the original equation, so the correct answer is (2).
Embark on a Quadratic Adventure: Finding the Equivalent Equation!
The question is: Which equation has the same solution as x² – 6x + 9 = 0?
The answer choices are:
- (1) (x + 3)² = 0
- (2) (x – 3)² = 0
- (3) (x + 3)² = 9
- (4) (x – 3)² = 9
Let’s find the correct answer by expanding option (2):
(x – 3)² = 0 ⟶ (x – 3)(x – 3) = 0 ⟶ x² – 6x + 9 = 0
This matches the original equation, so the correct answer is (2).
Explore the World of Quadratics: Uncovering the Hidden Equation!
The question is: Which equation has the same solution as x² – 4x – 5 = 0?
The answer choices are:
- (1) (x + 1)² = 20
- (2) (x – 1)² = 20
- (3) (x + 1)² = 24
- (4) (x – 1)² = 24
Let’s find the correct answer by expanding option (4):
(x – 1)² = 24 ⟶ (x – 1)(x – 1) = 24 ⟶ x² – 2x + 1 = 24 ⟶ x² – 2x – 23 = 0
This doesn’t match the original equation, so let’s try option (2):
(x – 1)² = 20 ⟶ (x – 1)(x – 1) = 20 ⟶ x² – 2x + 1 = 20 ⟶ x² – 2x – 19 = 0
This doesn’t match either, so let’s try option (1):
(x + 1)² = 20 ⟶ (x + 1)(x + 1) = 20 ⟶ x² + 2x + 1 = 20 ⟶ x² + 2x – 19 = 0
None of the options match the original equation, so it appears there may be an error in the question or answer choices.