Question

16) Review: Solve 2x2 + 4x - 5 = 0 by completing the square. Hint: First two steps: Add 5 to both sides and then divide all terms by 2. Then, take half of coefficient on x. Square it. Add this amount to both sides. Factor and then solve by extracting square roots.

Answer 1

2x^2 + 4x - 5 = 0

adding 5 on both sides

2x^2 + 4x = 5

dividing both sides by 2

x^2 + 2x = 5/2

take half of x term coefficient and square it

add this value on both sides

x^2 + 2x + 1 = 5/2 + 1

making left hand side a perfect square

( x + 1 )^2 = 7/2

taking square root pn both sides

sqrt ( x+1)^2 = sqrt ( 7/2 )

x + 1 = +- sqrt ( 7/2)

subtracting 1 from both sides

x = -1 +- sqrt ( 7/2)

solutions are

x = -1 + sqrt (7/2) , -1 - sqrt (7/2)

or

x = -1 + sqrt (14) / 2 , -1 - sqrt (14) / 2