Asked by Linda Samuelraj on May 21, 2024
Verified
Solve x2−8x−9=0x ^ { 2 } - 8 x - 9 = 0x2−8x−9=0 by completing the square, if possible.
A) x=−1,x=9x = - 1 , x = 9x=−1,x=9
B) x=8,x=−9x = 8 , x = - 9x=8,x=−9
C) x=1,x=−9x = 1 , x = - 9x=1,x=−9
D) x=−8,x=−9x = - 8 , x = - 9x=−8,x=−9
E) no solutions
Completing The Square
A method used in algebra to solve quadratic equations by converting the equation to a perfect square trinomial.
- Master the technique of solving quadratic equations through the process of completing the square.
Verified Answer
SB
SUSHANT BISTAMay 25, 2024
Final Answer :
A
Explanation :
To solve the equation x2−8x−9=0x^2 - 8x - 9 = 0x2−8x−9=0 by completing the square, we first move the constant term to the other side: x2−8x=9x^2 - 8x = 9x2−8x=9 . Then, we add (−82)2=16(\frac{-8}{2})^2 = 16(2−8)2=16 to both sides to complete the square: x2−8x+16=25x^2 - 8x + 16 = 25x2−8x+16=25 . This gives us (x−4)2=25(x - 4)^2 = 25(x−4)2=25 . Taking the square root of both sides gives x−4=±5x - 4 = \pm5x−4=±5 , leading to x=4+5=9x = 4 + 5 = 9x=4+5=9 and x=4−5=−1x = 4 - 5 = -1x=4−5=−1 .
Learning Objectives
- Master the technique of solving quadratic equations through the process of completing the square.