Solve for x
x=\sqrt{7}\approx 2.645751311
x=-\sqrt{7}\approx -2.645751311
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Polynomial
5 problems similar to:
\frac{ 3x }{ 5 } (1-x)+ \frac{ x+4 }{ 2 } = \frac{ 11(x-2) }{ 10 }
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2\times 3x\left(1-x\right)+5\left(x+4\right)=11\left(x-2\right)
Multiply both sides of the equation by 10, the least common multiple of 5,2,10.
6x\left(1-x\right)+5\left(x+4\right)=11\left(x-2\right)
Multiply 2 and 3 to get 6.
6x-6x^{2}+5\left(x+4\right)=11\left(x-2\right)
Use the distributive property to multiply 6x by 1-x.
6x-6x^{2}+5x+20=11\left(x-2\right)
Use the distributive property to multiply 5 by x+4.
11x-6x^{2}+20=11\left(x-2\right)
Combine 6x and 5x to get 11x.
11x-6x^{2}+20=11x-22
Use the distributive property to multiply 11 by x-2.
11x-6x^{2}+20-11x=-22
Subtract 11x from both sides.
-6x^{2}+20=-22
Combine 11x and -11x to get 0.
-6x^{2}=-22-20
Subtract 20 from both sides.
-6x^{2}=-42
Subtract 20 from -22 to get -42.
x^{2}=\frac{-42}{-6}
Divide both sides by -6.
x^{2}=7
Divide -42 by -6 to get 7.
x=\sqrt{7} x=-\sqrt{7}
Take the square root of both sides of the equation.
2\times 3x\left(1-x\right)+5\left(x+4\right)=11\left(x-2\right)
Multiply both sides of the equation by 10, the least common multiple of 5,2,10.
6x\left(1-x\right)+5\left(x+4\right)=11\left(x-2\right)
Multiply 2 and 3 to get 6.
6x-6x^{2}+5\left(x+4\right)=11\left(x-2\right)
Use the distributive property to multiply 6x by 1-x.
6x-6x^{2}+5x+20=11\left(x-2\right)
Use the distributive property to multiply 5 by x+4.
11x-6x^{2}+20=11\left(x-2\right)
Combine 6x and 5x to get 11x.
11x-6x^{2}+20=11x-22
Use the distributive property to multiply 11 by x-2.
11x-6x^{2}+20-11x=-22
Subtract 11x from both sides.
-6x^{2}+20=-22
Combine 11x and -11x to get 0.
-6x^{2}+20+22=0
Add 22 to both sides.
-6x^{2}+42=0
Add 20 and 22 to get 42.
x=\frac{0±\sqrt{0^{2}-4\left(-6\right)\times 42}}{2\left(-6\right)}
This equation is in standard form: ax^{2}+bx+c=0. Substitute -6 for a, 0 for b, and 42 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{0±\sqrt{-4\left(-6\right)\times 42}}{2\left(-6\right)}
Square 0.
x=\frac{0±\sqrt{24\times 42}}{2\left(-6\right)}
Multiply -4 times -6.
x=\frac{0±\sqrt{1008}}{2\left(-6\right)}
Multiply 24 times 42.
x=\frac{0±12\sqrt{7}}{2\left(-6\right)}
Take the square root of 1008.
x=\frac{0±12\sqrt{7}}{-12}
Multiply 2 times -6.
x=-\sqrt{7}
Now solve the equation x=\frac{0±12\sqrt{7}}{-12} when ± is plus.
x=\sqrt{7}
Now solve the equation x=\frac{0±12\sqrt{7}}{-12} when ± is minus.
x=-\sqrt{7} x=\sqrt{7}
The equation is now solved.
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y = 3x + 4
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Matrix
\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]
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
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}