Solving for a variable can be extremely daunting--especially in a multivariable equation such as 5x2−x=8y2+9xy4. 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.
5x2−x=8y2+9xy4⇒8y2+9x4y−5x2+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.
8y2+9x4y−5x2+x=0⇒32y2+9xy−20x2+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=−20x2+4xy1,2=−b±√b2−4ac2a | The only thing left to do is plug in the numbers. |
y1,2=−9x±√(9x)2−4∗32(−20x2+4x)2∗32 | It is time to simplify. |
y1,2=−9x±√81x2−128(−20x2+4x)64 | |
y1,2=−9x±√81x2+2560x2−512x64 | |
y1,2=−9x±√2641x2−512x64 | I have now successfully solve for y. |
Solving for a variable can be extremely daunting--especially in a multivariable equation such as 5x2−x=8y2+9xy4. 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.
5x2−x=8y2+9xy4⇒8y2+9x4y−5x2+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.
8y2+9x4y−5x2+x=0⇒32y2+9xy−20x2+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=−20x2+4xy1,2=−b±√b2−4ac2a | The only thing left to do is plug in the numbers. |
y1,2=−9x±√(9x)2−4∗32(−20x2+4x)2∗32 | It is time to simplify. |
y1,2=−9x±√81x2−128(−20x2+4x)64 | |
y1,2=−9x±√81x2+2560x2−512x64 | |
y1,2=−9x±√2641x2−512x64 | I have now successfully solve for y. |