Answer:
a = 10; a = 2
Step-by-step explanation:
Step 1: Use the Pythagorean theorem to solve this equation
1. Orignal eqaution: (a + 2)² + (a - 5)² = (a + 3)²
2. Expand (a + 2)² + (a - 5)² which will give us 2a² - 6a + 29
3. Expand (a + 3)² giving us a² + 6a + 9
4. Simplified equation: 2a² - 6a + 29 = a² + 6a + 9
Step 2: Subtract 9 from both sides
1. 2a² - 6a + 29 - 9 = a² + 6a + 9 - 9
2. Simplify: 2a² - 6a + 20 = a² + 6a
Step 3: Subtract 6a from both sides
1. 2a² - 6a + 20 - 6a = a² + 6a - 6a
2. Simplify: 2a² -12a + 20 = a²
Step 4: Subtract a2 from both sides
1. 2a² - 12a + 20 - a² = a² - a²
2. Simplify: a² - 12a + 20 = 0
Step 5: Use the quadratic formula to solve for a
1. Quadratic formula: a = -b += √b² - 4ac/2a
2. Plug in the correct values: a = -(-12) += √(-12)² + 4(1)(20)/2(1)
3. Simplify the numerator and denominator: 12 += 8/2
4. Final equation: a = 12 - 8/2 or a = 12 + 8/2
5. Hence, the answer is 10 or 2
