To solve the quadratic equation b^2 -5b -14 = 0 by completing the square, we follow these steps:
Step 1: Move the constant term (-14) to the other side of the equation:
b^2 - 5b = 14
Step 2: Take half of the coefficient of the linear term (-5/2) and square it to get the constant we will add and subtract in the equation:
(-5/2)^2 = 25/4
Step 3: Add the constant (25/4) to both sides of the equation:
b^2 - 5b + 25/4 = 14 + 25/4
Step 4: Simplify the equation:
(b - 5/2)^2 = 56/4 + 25/4
(b - 5/2)^2 = 81/4
Step 5: Take the square root of both sides of the equation:
b - 5/2 = ±√(81/4)
Step 6: Simplify the square root expression:
b - 5/2 = ±(9/2)
Step 7: Solve for b:
Case 1: b - 5/2 = 9/2
b = 9/2 + 5/2
b = 14/2
b = 7
Case 2: b - 5/2 = -9/2
b = -9/2 + 5/2
b = -4/2
b = -2
Therefore, the solutions to the quadratic equation b^2 -5b -14 = 0 are b = 7 and b = -2.
solve b^2-5b-14=0 by completing the square
1 answer