Solve for x
x=2\sqrt{7}-4\approx 1.291502622
x=-2\sqrt{7}-4\approx -9.291502622
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শেয়ার করুন
ক্লিপবোর্ডে কপি করা হয়েছে
-x^{2}-8x+12=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{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\left(-1\right)\times 12}}{2\left(-1\right)}
This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, -8 for b, and 12 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-\left(-8\right)±\sqrt{64-4\left(-1\right)\times 12}}{2\left(-1\right)}
Square -8.
x=\frac{-\left(-8\right)±\sqrt{64+4\times 12}}{2\left(-1\right)}
Multiply -4 times -1.
x=\frac{-\left(-8\right)±\sqrt{64+48}}{2\left(-1\right)}
Multiply 4 times 12.
x=\frac{-\left(-8\right)±\sqrt{112}}{2\left(-1\right)}
Add 64 to 48.
x=\frac{-\left(-8\right)±4\sqrt{7}}{2\left(-1\right)}
Take the square root of 112.
x=\frac{8±4\sqrt{7}}{2\left(-1\right)}
The opposite of -8 is 8.
x=\frac{8±4\sqrt{7}}{-2}
Multiply 2 times -1.
x=\frac{4\sqrt{7}+8}{-2}
Now solve the equation x=\frac{8±4\sqrt{7}}{-2} when ± is plus. Add 8 to 4\sqrt{7}.
x=-2\sqrt{7}-4
Divide 8+4\sqrt{7} by -2.
x=\frac{8-4\sqrt{7}}{-2}
Now solve the equation x=\frac{8±4\sqrt{7}}{-2} when ± is minus. Subtract 4\sqrt{7} from 8.
x=2\sqrt{7}-4
Divide 8-4\sqrt{7} by -2.
x=-2\sqrt{7}-4 x=2\sqrt{7}-4
The equation is now solved.
-x^{2}-8x+12=0
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.
-x^{2}-8x+12-12=-12
Subtract 12 from both sides of the equation.
-x^{2}-8x=-12
Subtracting 12 from itself leaves 0.
\frac{-x^{2}-8x}{-1}=-\frac{12}{-1}
Divide both sides by -1.
x^{2}+\left(-\frac{8}{-1}\right)x=-\frac{12}{-1}
Dividing by -1 undoes the multiplication by -1.
x^{2}+8x=-\frac{12}{-1}
Divide -8 by -1.
x^{2}+8x=12
Divide -12 by -1.
x^{2}+8x+4^{2}=12+4^{2}
Divide 8, the coefficient of the x term, by 2 to get 4. Then add the square of 4 to both sides of the equation. This step makes the left hand side of the equation a perfect square.
x^{2}+8x+16=12+16
Square 4.
x^{2}+8x+16=28
Add 12 to 16.
\left(x+4\right)^{2}=28
Factor x^{2}+8x+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+4\right)^{2}}=\sqrt{28}
Take the square root of both sides of the equation.
x+4=2\sqrt{7} x+4=-2\sqrt{7}
Simplify.
x=2\sqrt{7}-4 x=-2\sqrt{7}-4
Subtract 4 from both sides of the equation.
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