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5x2-x= 8y2+9x / 4y

 Jun 27, 2018

Best Answer 

 #1
avatar+2340 
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Solving for a variable can be extremely daunting--especially in a multivariable equation such as \(5x^2-x=8y^2+\frac{9xy}{4}\). I have a few suggestions that may make this easier to do. 

 

1. Move everything to One Side of the Equation. 

 

This is a relatively simple step.

 

\(5x^2-x=8y^2+\frac{9xy}{4}\Rightarrow8y^2+\frac{9x}{4}y-5x^2+x=0\)

 

2. Eliminate All Instances of Fractions or Decimals 

 

Fractions can be pesky, and there is no reason to make a hard situation worse. In this case, we can multiply both sides of the equation by 4 to eliminate the fractions. In a situation like this one, this is also relatively easy to do. 

 

\(8y^2+\frac{9x}{4}y-5x^2+x=0\Rightarrow32y^2+9xy-20x^2+4x=0\)

 

3. Use a Formula to Finish it Off

 

This is written in the form of a quadratic, so the quadratic formula is the way to go. 

 

\(a=32; b=9x;c=-20x^2+4x\\ y_{1,2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\) The only thing left to do is plug in the numbers. 
\(y_{1,2}=\frac{-9x\pm\sqrt{(9x)^2-4*32(-20x^2+4x)}}{2*32}\) It is time to simplify. 
\(y_{1,2}=\frac{-9x\pm\sqrt{81x^2-128(-20x^2+4x)}}{64}\)  
\(y_{1,2}=\frac{-9x\pm\sqrt{81x^2+2560x^2-512x}}{64}\)  
\(y_{1,2}=\frac{-9x\pm\sqrt{2641x^2-512x}}{64}\) I have now successfully solve for y.
   


 

 Jun 27, 2018
 #1
avatar+2340 
+2
Best Answer

Solving for a variable can be extremely daunting--especially in a multivariable equation such as \(5x^2-x=8y^2+\frac{9xy}{4}\). I have a few suggestions that may make this easier to do. 

 

1. Move everything to One Side of the Equation. 

 

This is a relatively simple step.

 

\(5x^2-x=8y^2+\frac{9xy}{4}\Rightarrow8y^2+\frac{9x}{4}y-5x^2+x=0\)

 

2. Eliminate All Instances of Fractions or Decimals 

 

Fractions can be pesky, and there is no reason to make a hard situation worse. In this case, we can multiply both sides of the equation by 4 to eliminate the fractions. In a situation like this one, this is also relatively easy to do. 

 

\(8y^2+\frac{9x}{4}y-5x^2+x=0\Rightarrow32y^2+9xy-20x^2+4x=0\)

 

3. Use a Formula to Finish it Off

 

This is written in the form of a quadratic, so the quadratic formula is the way to go. 

 

\(a=32; b=9x;c=-20x^2+4x\\ y_{1,2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\) The only thing left to do is plug in the numbers. 
\(y_{1,2}=\frac{-9x\pm\sqrt{(9x)^2-4*32(-20x^2+4x)}}{2*32}\) It is time to simplify. 
\(y_{1,2}=\frac{-9x\pm\sqrt{81x^2-128(-20x^2+4x)}}{64}\)  
\(y_{1,2}=\frac{-9x\pm\sqrt{81x^2+2560x^2-512x}}{64}\)  
\(y_{1,2}=\frac{-9x\pm\sqrt{2641x^2-512x}}{64}\) I have now successfully solve for y.
   


 

TheXSquaredFactor Jun 27, 2018

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