Solve for x
x=20\sqrt{39}-140\approx -15.100040032
x=-20\sqrt{39}-140\approx -264.899959968
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-x^{2}-280x-4000=0
Multiply both sides of the equation by 2.
x=\frac{-\left(-280\right)±\sqrt{\left(-280\right)^{2}-4\left(-1\right)\left(-4000\right)}}{2\left(-1\right)}
This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, -280 for b, and -4000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-\left(-280\right)±\sqrt{78400-4\left(-1\right)\left(-4000\right)}}{2\left(-1\right)}
Square -280.
x=\frac{-\left(-280\right)±\sqrt{78400+4\left(-4000\right)}}{2\left(-1\right)}
Multiply -4 times -1.
x=\frac{-\left(-280\right)±\sqrt{78400-16000}}{2\left(-1\right)}
Multiply 4 times -4000.
x=\frac{-\left(-280\right)±\sqrt{62400}}{2\left(-1\right)}
Add 78400 to -16000.
x=\frac{-\left(-280\right)±40\sqrt{39}}{2\left(-1\right)}
Take the square root of 62400.
x=\frac{280±40\sqrt{39}}{2\left(-1\right)}
The opposite of -280 is 280.
x=\frac{280±40\sqrt{39}}{-2}
Multiply 2 times -1.
x=\frac{40\sqrt{39}+280}{-2}
Now solve the equation x=\frac{280±40\sqrt{39}}{-2} when ± is plus. Add 280 to 40\sqrt{39}.
x=-20\sqrt{39}-140
Divide 280+40\sqrt{39} by -2.
x=\frac{280-40\sqrt{39}}{-2}
Now solve the equation x=\frac{280±40\sqrt{39}}{-2} when ± is minus. Subtract 40\sqrt{39} from 280.
x=20\sqrt{39}-140
Divide 280-40\sqrt{39} by -2.
x=-20\sqrt{39}-140 x=20\sqrt{39}-140
The equation is now solved.
-x^{2}-280x-4000=0
Multiply both sides of the equation by 2.
-x^{2}-280x=4000
Add 4000 to both sides. Anything plus zero gives itself.
\frac{-x^{2}-280x}{-1}=\frac{4000}{-1}
Divide both sides by -1.
x^{2}+\left(-\frac{280}{-1}\right)x=\frac{4000}{-1}
Dividing by -1 undoes the multiplication by -1.
x^{2}+280x=\frac{4000}{-1}
Divide -280 by -1.
x^{2}+280x=-4000
Divide 4000 by -1.
x^{2}+280x+140^{2}=-4000+140^{2}
Divide 280, the coefficient of the x term, by 2 to get 140. Then add the square of 140 to both sides of the equation. This step makes the left hand side of the equation a perfect square.
x^{2}+280x+19600=-4000+19600
Square 140.
x^{2}+280x+19600=15600
Add -4000 to 19600.
\left(x+140\right)^{2}=15600
Factor x^{2}+280x+19600. 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+140\right)^{2}}=\sqrt{15600}
Take the square root of both sides of the equation.
x+140=20\sqrt{39} x+140=-20\sqrt{39}
Simplify.
x=20\sqrt{39}-140 x=-20\sqrt{39}-140
Subtract 140 from both sides of the equation.
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