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\left(8x-2\right)\left(3-x\right)=5
Use the distributive property to multiply 2 by 4x-1.
26x-8x^{2}-6=5
Use the distributive property to multiply 8x-2 by 3-x and combine like terms.
26x-8x^{2}-6-5=0
Subtract 5 from both sides.
26x-8x^{2}-11=0
Subtract 5 from -6 to get -11.
-8x^{2}+26x-11=0
All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.
x=\frac{-26±\sqrt{26^{2}-4\left(-8\right)\left(-11\right)}}{2\left(-8\right)}
This equation is in standard form: ax^{2}+bx+c=0. Substitute -8 for a, 26 for b, and -11 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-26±\sqrt{676-4\left(-8\right)\left(-11\right)}}{2\left(-8\right)}
Square 26.
x=\frac{-26±\sqrt{676+32\left(-11\right)}}{2\left(-8\right)}
Multiply -4 times -8.
x=\frac{-26±\sqrt{676-352}}{2\left(-8\right)}
Multiply 32 times -11.
x=\frac{-26±\sqrt{324}}{2\left(-8\right)}
Add 676 to -352.
x=\frac{-26±18}{2\left(-8\right)}
Take the square root of 324.
x=\frac{-26±18}{-16}
Multiply 2 times -8.
x=-\frac{8}{-16}
Now solve the equation x=\frac{-26±18}{-16} when ± is plus. Add -26 to 18.
x=\frac{1}{2}
Reduce the fraction \frac{-8}{-16} to lowest terms by extracting and canceling out 8.
x=-\frac{44}{-16}
Now solve the equation x=\frac{-26±18}{-16} when ± is minus. Subtract 18 from -26.
x=\frac{11}{4}
Reduce the fraction \frac{-44}{-16} to lowest terms by extracting and canceling out 4.
x=\frac{1}{2} x=\frac{11}{4}
The equation is now solved.
\left(8x-2\right)\left(3-x\right)=5
Use the distributive property to multiply 2 by 4x-1.
26x-8x^{2}-6=5
Use the distributive property to multiply 8x-2 by 3-x and combine like terms.
26x-8x^{2}=5+6
Add 6 to both sides.
26x-8x^{2}=11
Add 5 and 6 to get 11.
-8x^{2}+26x=11
Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.
\frac{-8x^{2}+26x}{-8}=\frac{11}{-8}
Divide both sides by -8.
x^{2}+\frac{26}{-8}x=\frac{11}{-8}
Dividing by -8 undoes the multiplication by -8.
x^{2}-\frac{13}{4}x=\frac{11}{-8}
Reduce the fraction \frac{26}{-8} to lowest terms by extracting and canceling out 2.
x^{2}-\frac{13}{4}x=-\frac{11}{8}
Divide 11 by -8.
x^{2}-\frac{13}{4}x+\left(-\frac{13}{8}\right)^{2}=-\frac{11}{8}+\left(-\frac{13}{8}\right)^{2}
Divide -\frac{13}{4}, the coefficient of the x term, by 2 to get -\frac{13}{8}. Then add the square of -\frac{13}{8} to both sides of the equation. This step makes the left hand side of the equation a perfect square.
x^{2}-\frac{13}{4}x+\frac{169}{64}=-\frac{11}{8}+\frac{169}{64}
Square -\frac{13}{8} by squaring both the numerator and the denominator of the fraction.
x^{2}-\frac{13}{4}x+\frac{169}{64}=\frac{81}{64}
Add -\frac{11}{8} to \frac{169}{64} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.
\left(x-\frac{13}{8}\right)^{2}=\frac{81}{64}
Factor x^{2}-\frac{13}{4}x+\frac{169}{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{13}{8}\right)^{2}}=\sqrt{\frac{81}{64}}
Take the square root of both sides of the equation.
x-\frac{13}{8}=\frac{9}{8} x-\frac{13}{8}=-\frac{9}{8}
Simplify.
x=\frac{11}{4} x=\frac{1}{2}
Add \frac{13}{8} to both sides of the equation.