Completing the square if a
- 2. Example 1. Solve 2x2 + 4x – 16 = 0 Steps Solution 1. Isolate the constant term to the right side of the equation. Write in the form of ax2 + bx = c 2x2 + 4x = 16 2. Divide each term by the coefficient of x2. The coefficient of x2 is 2. 2x2 2 + 4𝑥 2 = 16 2 x2 + 2x = 8
- 3. Steps Solution 3. Get the square of the half of x and add both sides of the equation. x2 + 2x = 8 2 2 = 1 ; (1)2 = 1 x2 + 2x + 1 = 8 + 1 x2 + 2x + 1 = 9 (x + 1)2 = 9 4. Apply the Square Root Property. (Square both sides) x + 1)2 = 9 x + 1 = ±3 5. Solve for the roots. x + 1 = ±3 x + 1 = 3 and x + 1 = -3 x = 3 - 1 and x = -3 - 1 x = 2 and x = -4
- 4. Example 2. Solve for the roots of 2x2 – 8x = 120 Steps Solution 1. Isolate the constant term to the right side of the equation. Write in the form of ax2 + bx = c 2x2 – 8x = 120 2. Divide each term by the coefficient of x2. The coefficient of x2 is 2. 2x2 2 - 8𝑥 2 = 120 2 x2 – 4x = 60
- 5. Steps Solution 3. Get the square of the half of x and add both sides of the equation. x2 – 4x = 60 = −4 2 = -2 = (-2)2 = 4 x2 – 4x + 4 = 60 + 4 x2 – 4x + 4 = 64 (x – 2)2 = 64 4. Apply the Square Root Property. (Square both sides) (x – 2)2 = 64 x - 2 = ±8 5. Solve for the roots. x – 2 = 8 and x – 2 = -8 x = 8 + 2 and x = -8 + 2 x = 10 and x = -6
- 6. Example 3. Find the solution set of 3x2 + 48 = -30x. Steps Solution 1. Isolate the constant term to the right side of the equation. Write in the form of ax2 + bx = c 3x2 + 30x = -48 2. Divide each term by the coefficient of x2. The coefficient of x2 is 3. 3x2 3 + 30𝑥 3 = −48 3 x2 + 10x = -16
- 7. Steps Solution 3. Get the square of the half of x and add both sides of the equation. x2 + 10x = -16 10 2 = 5 (5)2 = 25 x2 + 10x + 25 = -16 + 25 (x + 5)2 = 9 4. Apply the Square Root Property. (Square both sides) (x + 5)2 = 9 x + 5 = ±3 5. Solve for the roots. x + 5 = 3 and x + 5 = -3 x = 3 – 5 and x = -3 – 5 x = -2 and x = -8
- 8. Checking: 3x2 + 48 = -30x If x = -2 3(-2)2 + 48 = -30(-2) 3(4) + 48 = 60 12 + 48 = 60 60 = 60 If x = -8 3(-8)2 + 48 = -30(-8) 3(64) + 48 = 240 192 + 48 = 240 240 = 240