Final Answer
$y=\frac{3}{2}+\sqrt{-x+\frac{9}{4}},\:y=\frac{3}{2}-\sqrt{-x+\frac{9}{4}}$
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Step-by-step Solution
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1
We need to isolate the dependent variable , we can do that by simultaneously subtracting $x$ from both sides of the equation
$y\left(y-3\right)=-x$
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$y\left(y-3\right)=-x$
Learn how to solve problems step by step online. Solve the equation y(y-3)+x=0. We need to isolate the dependent variable , we can do that by simultaneously subtracting x from both sides of the equation. Solve the product y\left(y-3\right). Factor the polynomial y^2-3y. Add and subtract \left(\frac{b}{2}\right)^2, replacing b by it's value -3. Now, we can factor y^2+-3x+\frac{9}{4} as a squared binomial of the form \left(x+\frac{b}{2}\right)^2.
Final Answer
$y=\frac{3}{2}+\sqrt{-x+\frac{9}{4}},\:y=\frac{3}{2}-\sqrt{-x+\frac{9}{4}}$