Solve for x
x=\frac{\sqrt{57390}}{250}-0.9\approx 0.058248402
x=-\frac{\sqrt{57390}}{250}-0.9\approx -1.858248402
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x^{2}+1.8x-0.10824=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{-1.8±\sqrt{1.8^{2}-4\left(-0.10824\right)}}{2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 1.8 for b, and -0.10824 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-1.8±\sqrt{3.24-4\left(-0.10824\right)}}{2}
Square 1.8 by squaring both the numerator and the denominator of the fraction.
x=\frac{-1.8±\sqrt{3.24+0.43296}}{2}
Multiply -4 times -0.10824.
x=\frac{-1.8±\sqrt{3.67296}}{2}
Add 3.24 to 0.43296 by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.
x=\frac{-1.8±\frac{\sqrt{57390}}{125}}{2}
Take the square root of 3.67296.
x=\frac{\frac{\sqrt{57390}}{125}-\frac{9}{5}}{2}
Now solve the equation x=\frac{-1.8±\frac{\sqrt{57390}}{125}}{2} when ± is plus. Add -1.8 to \frac{\sqrt{57390}}{125}.
x=\frac{\sqrt{57390}}{250}-\frac{9}{10}
Divide -\frac{9}{5}+\frac{\sqrt{57390}}{125} by 2.
x=\frac{-\frac{\sqrt{57390}}{125}-\frac{9}{5}}{2}
Now solve the equation x=\frac{-1.8±\frac{\sqrt{57390}}{125}}{2} when ± is minus. Subtract \frac{\sqrt{57390}}{125} from -1.8.
x=-\frac{\sqrt{57390}}{250}-\frac{9}{10}
Divide -\frac{9}{5}-\frac{\sqrt{57390}}{125} by 2.
x=\frac{\sqrt{57390}}{250}-\frac{9}{10} x=-\frac{\sqrt{57390}}{250}-\frac{9}{10}
The equation is now solved.
x^{2}+1.8x-0.10824=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}+1.8x-0.10824-\left(-0.10824\right)=-\left(-0.10824\right)
Add 0.10824 to both sides of the equation.
x^{2}+1.8x=-\left(-0.10824\right)
Subtracting -0.10824 from itself leaves 0.
x^{2}+1.8x=0.10824
Subtract -0.10824 from 0.
x^{2}+1.8x+0.9^{2}=0.10824+0.9^{2}
Divide 1.8, the coefficient of the x term, by 2 to get 0.9. Then add the square of 0.9 to both sides of the equation. This step makes the left hand side of the equation a perfect square.
x^{2}+1.8x+0.81=0.10824+0.81
Square 0.9 by squaring both the numerator and the denominator of the fraction.
x^{2}+1.8x+0.81=0.91824
Add 0.10824 to 0.81 by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.
\left(x+0.9\right)^{2}=0.91824
Factor x^{2}+1.8x+0.81. 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+0.9\right)^{2}}=\sqrt{0.91824}
Take the square root of both sides of the equation.
x+0.9=\frac{\sqrt{57390}}{250} x+0.9=-\frac{\sqrt{57390}}{250}
Simplify.
x=\frac{\sqrt{57390}}{250}-\frac{9}{10} x=-\frac{\sqrt{57390}}{250}-\frac{9}{10}
Subtract 0.9 from both sides of the equation.
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4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
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Matrix
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Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
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