SOLUTION: 1- {{{5a^2-6a+1=0}}} 2- {{{2x-x^2=-24}}} 3- x^+3x=0 4- {{{6x(x-12)=0}}} 5- {{{4y^2+9-12y}}}

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: 1- {{{5a^2-6a+1=0}}} 2- {{{2x-x^2=-24}}} 3- x^+3x=0 4- {{{6x(x-12)=0}}} 5- {{{4y^2+9-12y}}}      Log On


   

Question 675969: 1- 5a%5E2-6a%2B1=0
2- 2x-x%5E2=-24
3- x^+3x=0
4- 6x%28x-12%29=0
5- 4y%5E2%2B9-12y
Answer by khv_maths(12) About Me  (Show Source):
You can put this solution on YOUR website!
1-
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: a=1,a=0.2.
  • Graphical form: Equation 5a%5E2-6a%2B1=0 was fully solved.
  • Text form: 5a^2-6a+1=0 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+5a%5E2-6a%2B1=0+%29
    For tutors: simplify_cartoon( 5a^2-6a+1=0 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+5%2Aa%5E2-6%2Aa%2B1+%29=0.
Equation highlight_red%28+5%2Aa%5E2-6%2Aa%2B1=0+%29 is a quadratic equation: 5*a^2-6*a+1 =0, and has solutions 1,0.2
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: a=1,a=0.2.

Universal Simplifier and Solver


Done!

2- 2x-x%5E2=-24 put it into ax%5E2%2Bbx%2Bc=0
so, -x%5E2%2B2x%2B24=0
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: x=-4,x=6.
  • Graphical form: Equation -x%5E2%2B2x%2B24=0 was fully solved.
  • Text form: -x^2+2x+24=0 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+-x%5E2%2B2x%2B24=0+%29
    For tutors: simplify_cartoon( -x^2+2x+24=0 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+-x%5E2%2B2%2Ax%2B24+%29=0.
Equation highlight_red%28+-x%5E2%2B2%2Ax%2B24=0+%29 is a quadratic equation: -x^2+2*x+24 =0, and has solutions -4,6
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=-4,x=6.

Universal Simplifier and Solver


Done!


3- x^+3x=0
??? x power what???

4- 6x%28x-12%29=0 put it into ax%5E2%2Bbx%2Bc=0
6x%28x-12%29=0 = 6x%5E2-72x=0
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: x=12,x=0.
  • Graphical form: Equation 6x%5E2-72x=0 was fully solved.
  • Text form: 6x^2-72x=0 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+6x%5E2-72x=0+%29
    For tutors: simplify_cartoon( 6x^2-72x=0 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+6%2Ax%5E2-72%2Ax+%29=0.
Equation highlight_red%28+6%2Ax%5E2-72%2Ax=0+%29 is a quadratic equation: 6*x^2-72*x =0, and has solutions 12,0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=12,x=0.

Universal Simplifier and Solver


Done!


5- 4y%5E2%2B9-12y
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: y=1.5,y=1.5.
  • Graphical form: Equation 4y%5E2%2B9-12y=0 was fully solved.
  • Text form: 4y^2+9-12y=0 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+4y%5E2%2B9-12y=0+%29
    For tutors: simplify_cartoon( 4y^2+9-12y=0 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 4%2Ay%5E2%2Bhighlight_red%28+9+%29-12%2Ay=0.
Moved 9 to the right of expression
It becomes 4%2Ay%5E2-12%2Ay%2Bhighlight_green%28+9+%29=0.
Look at highlight_red%28+4%2Ay%5E2-12%2Ay%2B9+%29=0.
Equation highlight_red%28+4%2Ay%5E2-12%2Ay%2B9=0+%29 is a quadratic equation: 4*y^2-12*y+9 =0, and has solutions 1.5,1.5
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: y=1.5,y=1.5.

Universal Simplifier and Solver


Done!