Solve for x
x=-1995
x=\frac{1}{2}=0.5
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2x^{2}+3989x+3987=5982
Use the distributive property to multiply x+1 by 2x+3987 and combine like terms.
2x^{2}+3989x+3987-5982=0
Subtract 5982 from both sides.
2x^{2}+3989x-1995=0
Subtract 5982 from 3987 to get -1995.
x=\frac{-3989±\sqrt{3989^{2}-4\times 2\left(-1995\right)}}{2\times 2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 3989 for b, and -1995 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-3989±\sqrt{15912121-4\times 2\left(-1995\right)}}{2\times 2}
Square 3989.
x=\frac{-3989±\sqrt{15912121-8\left(-1995\right)}}{2\times 2}
Multiply -4 times 2.
x=\frac{-3989±\sqrt{15912121+15960}}{2\times 2}
Multiply -8 times -1995.
x=\frac{-3989±\sqrt{15928081}}{2\times 2}
Add 15912121 to 15960.
x=\frac{-3989±3991}{2\times 2}
Take the square root of 15928081.
x=\frac{-3989±3991}{4}
Multiply 2 times 2.
x=\frac{2}{4}
Now solve the equation x=\frac{-3989±3991}{4} when ± is plus. Add -3989 to 3991.
x=\frac{1}{2}
Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.
x=-\frac{7980}{4}
Now solve the equation x=\frac{-3989±3991}{4} when ± is minus. Subtract 3991 from -3989.
x=-1995
Divide -7980 by 4.
x=\frac{1}{2} x=-1995
The equation is now solved.
2x^{2}+3989x+3987=5982
Use the distributive property to multiply x+1 by 2x+3987 and combine like terms.
2x^{2}+3989x=5982-3987
Subtract 3987 from both sides.
2x^{2}+3989x=1995
Subtract 3987 from 5982 to get 1995.
\frac{2x^{2}+3989x}{2}=\frac{1995}{2}
Divide both sides by 2.
x^{2}+\frac{3989}{2}x=\frac{1995}{2}
Dividing by 2 undoes the multiplication by 2.
x^{2}+\frac{3989}{2}x+\left(\frac{3989}{4}\right)^{2}=\frac{1995}{2}+\left(\frac{3989}{4}\right)^{2}
Divide \frac{3989}{2}, the coefficient of the x term, by 2 to get \frac{3989}{4}. Then add the square of \frac{3989}{4} to both sides of the equation. This step makes the left hand side of the equation a perfect square.
x^{2}+\frac{3989}{2}x+\frac{15912121}{16}=\frac{1995}{2}+\frac{15912121}{16}
Square \frac{3989}{4} by squaring both the numerator and the denominator of the fraction.
x^{2}+\frac{3989}{2}x+\frac{15912121}{16}=\frac{15928081}{16}
Add \frac{1995}{2} to \frac{15912121}{16} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.
\left(x+\frac{3989}{4}\right)^{2}=\frac{15928081}{16}
Factor x^{2}+\frac{3989}{2}x+\frac{15912121}{16}. 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{3989}{4}\right)^{2}}=\sqrt{\frac{15928081}{16}}
Take the square root of both sides of the equation.
x+\frac{3989}{4}=\frac{3991}{4} x+\frac{3989}{4}=-\frac{3991}{4}
Simplify.
x=\frac{1}{2} x=-1995
Subtract \frac{3989}{4} from both sides of the equation.
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