SOLUTION: Solve by completing the square. The equation is 25x^2+30-12=0

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Solve by completing the square. The equation is 25x^2+30-12=0      Log On


   



Question 1076346: Solve by completing the square. The equation is 25x^2+30-12=0
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

25x%5E2%2B30-12=0....I assume you forgot to put x after 30
%2825x%5E2%2B30x%29-12=0
25%28x%5E2%2B%2830%2F25%29x%29-12=0
25%28x%5E2%2B%286%2F5%29x%29-12=0.....recall the rule:%28a%2Bb%29%5E2=a%5E2%2B2ab%2Bb%5E2...in your case we need b%5E2 part to complete square
25%28x%5E2%2B%286%2F5%29x%2Bb%5E2%29-25%2Ab%5E2-12=0...we already have a=1 and 2ab=6%2F5 and we can calculate b
2%2A1%2Ab=6%2F5
b=%286%2F5%29%2F2
b=%28cross%286%293%2F5%29%2Fcross%282%291
b=3%2F5

25%28x%5E2%2B%286%2F5%29x%2B%283%2F5%29%5E2%29-25%2A%283%2F5%29%5E2-12=0
25%28x%5E2%2B%286%2F5%29x%2B9%2F25%29-cross%2825%29%2A%289%2Fcross%2825%29%29-12=0
25%28x%2B3%2F5%29%5E2-9-12=0
25%28x%2B3%2F5%29%5E2-21=0



Answer by MathTherapy(10556) About Me  (Show Source):
You can put this solution on YOUR website!

Solve by completing the square. The equation is 25x^2+30-12=0
If this is 25x%5E2+%2B+30x+-+12+=+0, then this is the correct way to solve by COMPLETING the square
x%5E2+%2B+%2830%2F25%29x+-+12%2F25+=+0 ------- Dividing by 25
x%5E2+%2B+%286%2F5%29x+=+12%2F25 ------- Reducing 30%2F25, and adding 12%2F25 to both sides
------ Taking %281%2F2%29 of b, squaring it, and then adding the result to both sides
x%5E2+%2B+%286%2F5%29x+%2B+%286%2F10%29%5E2+=+12%2F25+%2B+%286%2F10%29%5E2, reduced to: x%5E2+%2B+%286%2F5%29x+%2B+%283%2F5%29%5E2+=+12%2F25+%2B+%283%2F5%29%5E2
%28x+%2B+3%2F5%29%5E2+=+12%2F25+%2B+9%2F25
%28x+%2B+3%2F5%29%5E2+=+21%2F25
sqrt%28%28x+%2B+3%2F5%29%5E2%29+=+%22+%22%2B-+sqrt%2821%2F25%29 ------- Taking the square root of both sides
x+%2B+3%2F5+=+%22%22%2B-+sqrt%2821%29%2F5