Solve for x

x=3<br/>x=0

$x=3$

$x=0$

$x=0$

Steps Using Factoring

Steps Using the Quadratic Formula

Steps for Completing the Square

Graph

Graph Both Sides in 2D

Graph in 2D

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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.

Examples

Quadratic equation

{ x } ^ { 2 } - 4 x - 5 = 0

$x_{2}−4x−5=0$

Trigonometry

4 \sin \theta \cos \theta = 2 \sin \theta

$4sinθcosθ=2sinθ$

Linear equation

y = 3x + 4

$y=3x+4$

Arithmetic

699 * 533

$699∗533$

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]

$[25 34 ][2−1 01 35 ]$

Simultaneous equation

\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.

${8x+2y=467x+3y=47 $

Differentiation

\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }

$dxd (x−5)(3x_{2}−2) $

Integration

\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x

$∫_{0}xe_{−x_{2}}dx$

Limits

\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}

$x→−3lim x_{2}+2x−3x_{2}−9 $