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\frac{15000\left(-2x+1\right)^{2}}{15000}=\frac{12150}{15000}
Divide both sides by 15000.
\left(-2x+1\right)^{2}=\frac{12150}{15000}
Dividing by 15000 undoes the multiplication by 15000.
\left(-2x+1\right)^{2}=\frac{81}{100}
Reduce the fraction \frac{12150}{15000} to lowest terms by extracting and canceling out 150.
-2x+1=\frac{9}{10} -2x+1=-\frac{9}{10}
Take the square root of both sides of the equation.
-2x+1-1=\frac{9}{10}-1 -2x+1-1=-\frac{9}{10}-1
Subtract 1 from both sides of the equation.
-2x=\frac{9}{10}-1 -2x=-\frac{9}{10}-1
Subtracting 1 from itself leaves 0.
-2x=-\frac{1}{10}
Subtract 1 from \frac{9}{10}.
-2x=-\frac{19}{10}
Subtract 1 from -\frac{9}{10}.
\frac{-2x}{-2}=-\frac{\frac{1}{10}}{-2} \frac{-2x}{-2}=-\frac{\frac{19}{10}}{-2}
Divide both sides by -2.
x=-\frac{\frac{1}{10}}{-2} x=-\frac{\frac{19}{10}}{-2}
Dividing by -2 undoes the multiplication by -2.
x=\frac{1}{20}
Divide -\frac{1}{10} by -2.
x=\frac{19}{20}
Divide -\frac{19}{10} by -2.
x=\frac{1}{20} x=\frac{19}{20}
The equation is now solved.