Factor
-\left(x-\frac{-\sqrt{29}-3}{2}\right)\left(x-\frac{\sqrt{29}-3}{2}\right)
Evaluate
5-3x-x^{2}
গ্রাফ
শেয়ার করুন
ক্লিপবোর্ডে কপি করা হয়েছে
-x^{2}-3x+5=0
Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.
x=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\left(-1\right)\times 5}}{2\left(-1\right)}
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(-3\right)±\sqrt{9-4\left(-1\right)\times 5}}{2\left(-1\right)}
Square -3.
x=\frac{-\left(-3\right)±\sqrt{9+4\times 5}}{2\left(-1\right)}
Multiply -4 times -1.
x=\frac{-\left(-3\right)±\sqrt{9+20}}{2\left(-1\right)}
Multiply 4 times 5.
x=\frac{-\left(-3\right)±\sqrt{29}}{2\left(-1\right)}
Add 9 to 20.
x=\frac{3±\sqrt{29}}{2\left(-1\right)}
The opposite of -3 is 3.
x=\frac{3±\sqrt{29}}{-2}
Multiply 2 times -1.
x=\frac{\sqrt{29}+3}{-2}
Now solve the equation x=\frac{3±\sqrt{29}}{-2} when ± is plus. Add 3 to \sqrt{29}.
x=\frac{-\sqrt{29}-3}{2}
Divide 3+\sqrt{29} by -2.
x=\frac{3-\sqrt{29}}{-2}
Now solve the equation x=\frac{3±\sqrt{29}}{-2} when ± is minus. Subtract \sqrt{29} from 3.
x=\frac{\sqrt{29}-3}{2}
Divide 3-\sqrt{29} by -2.
-x^{2}-3x+5=-\left(x-\frac{-\sqrt{29}-3}{2}\right)\left(x-\frac{\sqrt{29}-3}{2}\right)
Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-3-\sqrt{29}}{2} for x_{1} and \frac{-3+\sqrt{29}}{2} for x_{2}.
উদাহরণ
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