Solve for x

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x^{2}+x^{2}-6x=0
Use the distributive property to multiply x by x-6.
2x^{2}-6x=0
Combine x^{2} and x^{2} to get 2x^{2}.
x\left(2x-6\right)=0
Factor out x.
x=0 x=3
To find equation solutions, solve x=0 and 2x-6=0.
x^{2}+x^{2}-6x=0
Use the distributive property to multiply x by x-6.
2x^{2}-6x=0
Combine x^{2} and x^{2} to get 2x^{2}.
x=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}}}{2\times 2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, -6 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-\left(-6\right)±6}{2\times 2}
Take the square root of \left(-6\right)^{2}\approx 36.
x=\frac{6±6}{2\times 2}
The opposite of -6 is 6.
x=\frac{6±6}{4}
Multiply 2 times 2.
x=\frac{12}{4}
Now solve the equation x=\frac{6±6}{4} when ± is plus. Add 6 to 6.
x=3
Divide 12 by 4.
x=\frac{0}{4}
Now solve the equation x=\frac{6±6}{4} when ± is minus. Subtract 6 from 6.
x=0
Divide 0 by 4.
x=3 x=0
The equation is now solved.
x^{2}+x^{2}-6x=0
Use the distributive property to multiply x by x-6.
2x^{2}-6x=0
Combine x^{2} and x^{2} to get 2x^{2}.
\frac{2x^{2}-6x}{2}=\frac{0}{2}
Divide both sides by 2.
x^{2}+\frac{-6}{2}x=\frac{0}{2}
Dividing by 2 undoes the multiplication by 2.
x^{2}-3x=\frac{0}{2}
Divide -6 by 2.
x^{2}-3x=0
Divide 0 by 2.
x^{2}-3x+\left(-\frac{3}{2}\right)^{2}=\left(-\frac{3}{2}\right)^{2}
Divide -3, the coefficient of the x term, by 2 to get -\frac{3}{2}=-1.5. Then add the square of -\frac{3}{2}=-1.5 to both sides of the equation. This step makes the left hand side of the equation a perfect square.
x^{2}-3x+\frac{9}{4}=\frac{9}{4}
Square -\frac{3}{2}=-1.5 by squaring both the numerator and the denominator of the fraction.
\left(x-\frac{3}{2}\right)^{2}=\frac{9}{4}
Factor x^{2}-3x+\frac{9}{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-\frac{3}{2}\right)^{2}}=\sqrt{\frac{9}{4}}
Take the square root of both sides of the equation.
x-\frac{3}{2}=\frac{3}{2} x-\frac{3}{2}=-\frac{3}{2}
Simplify.
x=3 x=0
Add \frac{3}{2}=1.5 to both sides of the equation.