Solve for x (complex solution)
x=\frac{\sqrt{3335}i}{160}+\frac{15}{32}\approx 0.46875+0.360934118i
x=-\frac{\sqrt{3335}i}{160}+\frac{15}{32}\approx 0.46875-0.360934118i
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4-10x-60=5\left(x-1\right)\times 32x
Use the distributive property to multiply -10 by x+6.
-56-10x=5\left(x-1\right)\times 32x
Subtract 60 from 4 to get -56.
-56-10x=160\left(x-1\right)x
Multiply 5 and 32 to get 160.
-56-10x=\left(160x-160\right)x
Use the distributive property to multiply 160 by x-1.
-56-10x=160x^{2}-160x
Use the distributive property to multiply 160x-160 by x.
-56-10x-160x^{2}=-160x
Subtract 160x^{2} from both sides.
-56-10x-160x^{2}+160x=0
Add 160x to both sides.
-56+150x-160x^{2}=0
Combine -10x and 160x to get 150x.
-160x^{2}+150x-56=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{-150±\sqrt{150^{2}-4\left(-160\right)\left(-56\right)}}{2\left(-160\right)}
This equation is in standard form: ax^{2}+bx+c=0. Substitute -160 for a, 150 for b, and -56 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-150±\sqrt{22500-4\left(-160\right)\left(-56\right)}}{2\left(-160\right)}
Square 150.
x=\frac{-150±\sqrt{22500+640\left(-56\right)}}{2\left(-160\right)}
Multiply -4 times -160.
x=\frac{-150±\sqrt{22500-35840}}{2\left(-160\right)}
Multiply 640 times -56.
x=\frac{-150±\sqrt{-13340}}{2\left(-160\right)}
Add 22500 to -35840.
x=\frac{-150±2\sqrt{3335}i}{2\left(-160\right)}
Take the square root of -13340.
x=\frac{-150±2\sqrt{3335}i}{-320}
Multiply 2 times -160.
x=\frac{-150+2\sqrt{3335}i}{-320}
Now solve the equation x=\frac{-150±2\sqrt{3335}i}{-320} when ± is plus. Add -150 to 2i\sqrt{3335}.
x=-\frac{\sqrt{3335}i}{160}+\frac{15}{32}
Divide -150+2i\sqrt{3335} by -320.
x=\frac{-2\sqrt{3335}i-150}{-320}
Now solve the equation x=\frac{-150±2\sqrt{3335}i}{-320} when ± is minus. Subtract 2i\sqrt{3335} from -150.
x=\frac{\sqrt{3335}i}{160}+\frac{15}{32}
Divide -150-2i\sqrt{3335} by -320.
x=-\frac{\sqrt{3335}i}{160}+\frac{15}{32} x=\frac{\sqrt{3335}i}{160}+\frac{15}{32}
The equation is now solved.
4-10x-60=5\left(x-1\right)\times 32x
Use the distributive property to multiply -10 by x+6.
-56-10x=5\left(x-1\right)\times 32x
Subtract 60 from 4 to get -56.
-56-10x=160\left(x-1\right)x
Multiply 5 and 32 to get 160.
-56-10x=\left(160x-160\right)x
Use the distributive property to multiply 160 by x-1.
-56-10x=160x^{2}-160x
Use the distributive property to multiply 160x-160 by x.
-56-10x-160x^{2}=-160x
Subtract 160x^{2} from both sides.
-56-10x-160x^{2}+160x=0
Add 160x to both sides.
-56+150x-160x^{2}=0
Combine -10x and 160x to get 150x.
150x-160x^{2}=56
Add 56 to both sides. Anything plus zero gives itself.
-160x^{2}+150x=56
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{-160x^{2}+150x}{-160}=\frac{56}{-160}
Divide both sides by -160.
x^{2}+\frac{150}{-160}x=\frac{56}{-160}
Dividing by -160 undoes the multiplication by -160.
x^{2}-\frac{15}{16}x=\frac{56}{-160}
Reduce the fraction \frac{150}{-160} to lowest terms by extracting and canceling out 10.
x^{2}-\frac{15}{16}x=-\frac{7}{20}
Reduce the fraction \frac{56}{-160} to lowest terms by extracting and canceling out 8.
x^{2}-\frac{15}{16}x+\left(-\frac{15}{32}\right)^{2}=-\frac{7}{20}+\left(-\frac{15}{32}\right)^{2}
Divide -\frac{15}{16}, the coefficient of the x term, by 2 to get -\frac{15}{32}. Then add the square of -\frac{15}{32} to both sides of the equation. This step makes the left hand side of the equation a perfect square.
x^{2}-\frac{15}{16}x+\frac{225}{1024}=-\frac{7}{20}+\frac{225}{1024}
Square -\frac{15}{32} by squaring both the numerator and the denominator of the fraction.
x^{2}-\frac{15}{16}x+\frac{225}{1024}=-\frac{667}{5120}
Add -\frac{7}{20} to \frac{225}{1024} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.
\left(x-\frac{15}{32}\right)^{2}=-\frac{667}{5120}
Factor x^{2}-\frac{15}{16}x+\frac{225}{1024}. 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{15}{32}\right)^{2}}=\sqrt{-\frac{667}{5120}}
Take the square root of both sides of the equation.
x-\frac{15}{32}=\frac{\sqrt{3335}i}{160} x-\frac{15}{32}=-\frac{\sqrt{3335}i}{160}
Simplify.
x=\frac{\sqrt{3335}i}{160}+\frac{15}{32} x=-\frac{\sqrt{3335}i}{160}+\frac{15}{32}
Add \frac{15}{32} to both sides of the equation.
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