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4x^{2}-2x=3-x
Use the distributive property to multiply 2x by 2x-1.
4x^{2}-2x-3=-x
Subtract 3 from both sides.
4x^{2}-2x-3+x=0
Add x to both sides.
4x^{2}-x-3=0
Combine -2x and x to get -x.
x=\frac{-\left(-1\right)±\sqrt{1-4\times 4\left(-3\right)}}{2\times 4}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, -1 for b, and -3 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-\left(-1\right)±\sqrt{1-16\left(-3\right)}}{2\times 4}
Multiply -4 times 4.
x=\frac{-\left(-1\right)±\sqrt{1+48}}{2\times 4}
Multiply -16 times -3.
x=\frac{-\left(-1\right)±\sqrt{49}}{2\times 4}
Add 1 to 48.
x=\frac{-\left(-1\right)±7}{2\times 4}
Take the square root of 49.
x=\frac{1±7}{2\times 4}
The opposite of -1 is 1.
x=\frac{1±7}{8}
Multiply 2 times 4.
x=\frac{8}{8}
Now solve the equation x=\frac{1±7}{8} when ± is plus. Add 1 to 7.
x=1
Divide 8 by 8.
x=-\frac{6}{8}
Now solve the equation x=\frac{1±7}{8} when ± is minus. Subtract 7 from 1.
x=-\frac{3}{4}
Reduce the fraction \frac{-6}{8} to lowest terms by extracting and canceling out 2.
x=1 x=-\frac{3}{4}
The equation is now solved.
4x^{2}-2x=3-x
Use the distributive property to multiply 2x by 2x-1.
4x^{2}-2x+x=3
Add x to both sides.
4x^{2}-x=3
Combine -2x and x to get -x.
\frac{4x^{2}-x}{4}=\frac{3}{4}
Divide both sides by 4.
x^{2}-\frac{1}{4}x=\frac{3}{4}
Dividing by 4 undoes the multiplication by 4.
x^{2}-\frac{1}{4}x+\left(-\frac{1}{8}\right)^{2}=\frac{3}{4}+\left(-\frac{1}{8}\right)^{2}
Divide -\frac{1}{4}, the coefficient of the x term, by 2 to get -\frac{1}{8}. Then add the square of -\frac{1}{8} to both sides of the equation. This step makes the left hand side of the equation a perfect square.
x^{2}-\frac{1}{4}x+\frac{1}{64}=\frac{3}{4}+\frac{1}{64}
Square -\frac{1}{8} by squaring both the numerator and the denominator of the fraction.
x^{2}-\frac{1}{4}x+\frac{1}{64}=\frac{49}{64}
Add \frac{3}{4} to \frac{1}{64} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.
\left(x-\frac{1}{8}\right)^{2}=\frac{49}{64}
Factor x^{2}-\frac{1}{4}x+\frac{1}{64}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.
\sqrt{\left(x-\frac{1}{8}\right)^{2}}=\sqrt{\frac{49}{64}}
Take the square root of both sides of the equation.
x-\frac{1}{8}=\frac{7}{8} x-\frac{1}{8}=-\frac{7}{8}
Simplify.
x=1 x=-\frac{3}{4}
Add \frac{1}{8} to both sides of the equation.