+2440 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. |
+2440 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. |
