Solve for x
x=\frac{\sqrt{43}}{2}-2\approx 1.278719262
x=-\frac{\sqrt{43}}{2}-2\approx -5.278719262
গ্রাফ
শেয়ার করুন
ক্লিপবোর্ডে কপি করা হয়েছে
x^{2}+4x=\frac{27}{4}
Multiply 9 and \frac{3}{4} to get \frac{27}{4}.
x^{2}+4x-\frac{27}{4}=0
Subtract \frac{27}{4} from both sides.
x=\frac{-4±\sqrt{4^{2}-4\left(-\frac{27}{4}\right)}}{2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 4 for b, and -\frac{27}{4} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-4±\sqrt{16-4\left(-\frac{27}{4}\right)}}{2}
Square 4.
x=\frac{-4±\sqrt{16+27}}{2}
Multiply -4 times -\frac{27}{4}.
x=\frac{-4±\sqrt{43}}{2}
Add 16 to 27.
x=\frac{\sqrt{43}-4}{2}
Now solve the equation x=\frac{-4±\sqrt{43}}{2} when ± is plus. Add -4 to \sqrt{43}.
x=\frac{\sqrt{43}}{2}-2
Divide -4+\sqrt{43} by 2.
x=\frac{-\sqrt{43}-4}{2}
Now solve the equation x=\frac{-4±\sqrt{43}}{2} when ± is minus. Subtract \sqrt{43} from -4.
x=-\frac{\sqrt{43}}{2}-2
Divide -4-\sqrt{43} by 2.
x=\frac{\sqrt{43}}{2}-2 x=-\frac{\sqrt{43}}{2}-2
The equation is now solved.
x^{2}+4x=\frac{27}{4}
Multiply 9 and \frac{3}{4} to get \frac{27}{4}.
x^{2}+4x+2^{2}=\frac{27}{4}+2^{2}
Divide 4, the coefficient of the x term, by 2 to get 2. Then add the square of 2 to both sides of the equation. This step makes the left hand side of the equation a perfect square.
x^{2}+4x+4=\frac{27}{4}+4
Square 2.
x^{2}+4x+4=\frac{43}{4}
Add \frac{27}{4} to 4.
\left(x+2\right)^{2}=\frac{43}{4}
Factor x^{2}+4x+4. 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+2\right)^{2}}=\sqrt{\frac{43}{4}}
Take the square root of both sides of the equation.
x+2=\frac{\sqrt{43}}{2} x+2=-\frac{\sqrt{43}}{2}
Simplify.
x=\frac{\sqrt{43}}{2}-2 x=-\frac{\sqrt{43}}{2}-2
Subtract 2 from both sides of the equation.
উদাহরণ
দ্বিঘাত সমীকরণ
{ x } ^ { 2 } - 4 x - 5 = 0
ত্রিকোণমিতি
4 \sin \theta \cos \theta = 2 \sin \theta
রৈখিক সমীকরণ
y = 3x + 4
পাটিগণিত
699 * 533
মেট্রিক্স
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
সমকালীন সমীকরণ
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
ডিফারেন্সিয়েশন
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
ইন্টিগ্রেশন
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
লিমিট
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}