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\frac{1}{2}x\times 2x+2xx=2\times 51
Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2x, the least common multiple of 2,x.
xx+2xx=2\times 51
Cancel out 2 and 2.
x^{2}+2xx=2\times 51
Multiply x and x to get x^{2}.
x^{2}+2x^{2}=2\times 51
Multiply x and x to get x^{2}.
3x^{2}=2\times 51
Combine x^{2} and 2x^{2} to get 3x^{2}.
3x^{2}=102
Multiply 2 and 51 to get 102.
x^{2}=\frac{102}{3}
Divide both sides by 3.
x^{2}=34
Divide 102 by 3 to get 34.
x=\sqrt{34} x=-\sqrt{34}
Take the square root of both sides of the equation.
\frac{1}{2}x\times 2x+2xx=2\times 51
Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2x, the least common multiple of 2,x.
xx+2xx=2\times 51
Cancel out 2 and 2.
x^{2}+2xx=2\times 51
Multiply x and x to get x^{2}.
x^{2}+2x^{2}=2\times 51
Multiply x and x to get x^{2}.
3x^{2}=2\times 51
Combine x^{2} and 2x^{2} to get 3x^{2}.
3x^{2}=102
Multiply 2 and 51 to get 102.
3x^{2}-102=0
Subtract 102 from both sides.
x=\frac{0±\sqrt{0^{2}-4\times 3\left(-102\right)}}{2\times 3}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -102 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{0±\sqrt{-4\times 3\left(-102\right)}}{2\times 3}
Square 0.
x=\frac{0±\sqrt{-12\left(-102\right)}}{2\times 3}
Multiply -4 times 3.
x=\frac{0±\sqrt{1224}}{2\times 3}
Multiply -12 times -102.
x=\frac{0±6\sqrt{34}}{2\times 3}
Take the square root of 1224.
x=\frac{0±6\sqrt{34}}{6}
Multiply 2 times 3.
x=\sqrt{34}
Now solve the equation x=\frac{0±6\sqrt{34}}{6} when ± is plus.
x=-\sqrt{34}
Now solve the equation x=\frac{0±6\sqrt{34}}{6} when ± is minus.
x=\sqrt{34} x=-\sqrt{34}
The equation is now solved.