Solve the Following Quadratic Equation by Factorization
Question:
\[ 3\sqrt{5}x^2+25x-10\sqrt{5}=0 \]Solution
Given:
\[ 3\sqrt{5}x^2+25x-10\sqrt{5}=0 \]Product of the coefficient of \(x^2\) and the constant term:
\[ (3\sqrt{5})(-10\sqrt{5})=-150 \]We split \(25x\) as \(30x-5x\):
\[ 3\sqrt{5}x^2+30x-5x-10\sqrt{5}=0 \] \[ 3\sqrt{5}x(x+2\sqrt{5})-5(x+2\sqrt{5})=0 \] \[ (x+2\sqrt{5})(3\sqrt{5}x-5)=0 \]Therefore,
\[ x+2\sqrt{5}=0 \quad \text{or} \quad 3\sqrt{5}x-5=0 \] \[ x=-2\sqrt{5} \] \[ x=\frac{5}{3\sqrt{5}} =\frac{\sqrt{5}}{3} \]