How do you solve by completing the square for 2x^2+10x-4=0?

2 Answers
Tash
Mar 13, 2018

2(x + 5/2)^2 - 33/2

Explanation:

Take 2 out of the equation:
2(x^2 + 5x - 2) = 0

Complete the square in the brackets:
2((x + 5/2)^2 - 25/4 - 2)

Simplify the equation:
2((x + 5/2)^2 - 33/4)
2(x + 5/2)^2 - 33/2

EZ as pi
Mar 13, 2018

2x^2 +10x -4=0

First divide by 2 so that we have 1x^2" "a=1

x^2 +5x -2=0

x^2 +5x " "=2" "larr move the constant to the RHS

x^2+5x+ (5/2)^2 = 2+(5/2)^2" "larr add (b/2)^2 to both sides.

By this process you have written the left side as a 'perfect square'
This step is the 'completing the square '- add in the missing term to create a square.

Write the left side as the square of a binomial.

(x+5/2)^2 = 4 1/2

x +5/2 = +-sqrt(9/2)" "larr find the square root of both sides.

Find the two possible solutions:

x = 3/(+sqrt2) -2.5 = -0.379 (3 dp)

x = 3/(-sqrt2)-2.5 = -4.624

Related questions
See all questions in Completing the Square
Impact of this question
6488 views around the world
You can reuse this answer
Creative Commons License