How do you solve the equation 2(x^2-5)=-x^2-12(x25)=x21?

1 Answer
Jun 8, 2017

x=+-sqrt(3)x=±3

Explanation:

Multiply the 22 through on the left hand side:

2(x^2-5)=-x^2-12(x25)=x21

2x^2-10=-x^2-12x210=x21

Add color(red)(x^2)x2 and color(blue)(10)10 to both sides

2x^2color(red)(+x^2)-10color(blue)(+10)=-x^2color(red)(+x^2)-1color(blue)(+10)2x2+x210+10=x2+x21+10

3x^2=93x2=9

Divide both sides by 33

(3x^2)/color(red)(3)=9/color(red)(3)3x23=93

x^2=3x2=3

Take sqrt(color(white)(aa))aa of both sides

color(red)(sqrt(color(black)(x^2))=color(red)(+-sqrt(color(black)(3))x2=±3

x=+-sqrt(3)x=±3