0 X 2 X 6

$6 \exponential{(10)}{2} - 6 x = 0 $

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x\left(6x-6\right)=0

Factor out x.

x=0 ten=1

To find equation solutions, solve ten=0 and 6x-6=0.

6x^{2}-6x=0

All equations of the form ax^{2}+bx+c=0 tin can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives 2 solutions, one when ± is improver and one when it is subtraction.

x=\frac{-\left(-half-dozen\correct)±\sqrt{\left(-6\right)^{2}}}{ii\times 6}

This equation is in standard grade: ax^{2}+bx+c=0. Substitute 6 for a, -6 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{ii}-4ac}}{2a}.

x=\frac{-\left(-half dozen\right)±6}{ii\times six}

Take the square root of \left(-six\right)^{2}.

x=\frac{vi±6}{2\times half-dozen}

The opposite of -six is six.

x=\frac{6±vi}{12}

Multiply ii times half dozen.

x=\frac{12}{12}

Now solve the equation x=\frac{6±6}{12} when ± is plus. Add together 6 to 6.

10=\frac{0}{12}

Now solve the equation x=\frac{6±6}{12} when ± is minus. Subtract 6 from 6.

ten=1 x=0

The equation is now solved.

6x^{2}-6x=0

Quadratic equations such every bit this one tin can be solved by completing the foursquare. In order to complete the square, the equation must first exist in the class x^{2}+bx=c.

\frac{6x^{2}-6x}{vi}=\frac{0}{half-dozen}

Divide both sides by 6.

x^{ii}+\frac{-6}{6}x=\frac{0}{half-dozen}

Dividing past 6 undoes the multiplication past 6.

x^{2}-x=\frac{0}{six}

Split up -6 by 6.

x^{ii}-ten+\left(-\frac{1}{2}\right)^{2}=\left(-\frac{1}{2}\right)^{ii}

Dissever -1, the coefficient of the ten term, past ii to become -\frac{ane}{2}. Then add together the square of -\frac{1}{2} to both sides of the equation. This step makes the left manus side of the equation a perfect square.

x^{2}-x+\frac{1}{4}=\frac{1}{4}

Square -\frac{1}{2} by squaring both the numerator and the denominator of the fraction.

\left(x-\frac{1}{2}\right)^{two}=\frac{i}{4}

Factor x^{two}-ten+\frac{1}{4}. In full general, when ten^{2}+bx+c is a perfect square, it tin can always exist factored as \left(x+\frac{b}{two}\right)^{2}.

\sqrt{\left(x-\frac{1}{2}\right)^{2}}=\sqrt{\frac{1}{iv}}

Take the foursquare root of both sides of the equation.

10-\frac{1}{2}=\frac{1}{ii} x-\frac{1}{2}=-\frac{ane}{2}

Simplify.

x=1 10=0

Add \frac{i}{2} to both sides of the equation.