Solve 6(1x^22)=5x

$$6(1 { x }^{ 2 } 2)=5x$$

Solve for x

$$x=\frac{5}{12}\approx 0.416666667$$

$$x=0$$

Steps Using Factoring

Multiply 6 and 1 to get 6.

$$6x^{2}\times 2=5x$$

Multiply 6 and 2 to get 12.

$$12x^{2}=5x$$

Subtract 5x from both sides.

$$12x^{2}-5x=0$$

Factor out x.

$$x\left(12x-5\right)=0$$

To find equation solutions, solve x=0 and 12x-5=0.

$$x=0 x=\frac{5}{12}$$

Steps Using the Quadratic Formula

Multiply 6 and 1 to get 6.

$$6x^{2}\times 2=5x$$

Multiply 6 and 2 to get 12.

$$12x^{2}=5x$$

Subtract 5x from both sides.

$$12x^{2}-5x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 12 for a, -5 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}}}{2\times 12}$$

Take the square root of \left(-5\right)^{2}.

$$x=\frac{-\left(-5\right)±5}{2\times 12}$$

The opposite of -5 is 5.

$$x=\frac{5±5}{2\times 12}$$

Multiply 2 times 12.

$$x=\frac{5±5}{24}$$

Now solve the equation x=\frac{5±5}{24} when ± is plus. Add 5 to 5.

$$x=\frac{10}{24}$$

Reduce the fraction \frac{10}{24} to lowest terms by extracting and canceling out 2.

$$x=\frac{5}{12}$$

Now solve the equation x=\frac{5±5}{24} when ± is minus. Subtract 5 from 5.

$$x=\frac{0}{24}$$

Divide 0 by 24.

$$x=0$$

The equation is now solved.

$$x=\frac{5}{12} x=0$$

Steps for Completing the Square

Multiply 6 and 1 to get 6.

$$6x^{2}\times 2=5x$$

Multiply 6 and 2 to get 12.

$$12x^{2}=5x$$

Subtract 5x from both sides.

$$12x^{2}-5x=0$$

Divide both sides by 12.

$$\frac{12x^{2}-5x}{12}=\frac{0}{12}$$

Dividing by 12 undoes the multiplication by 12.

$$x^{2}-\frac{5}{12}x=\frac{0}{12}$$

Divide 0 by 12.

$$x^{2}-\frac{5}{12}x=0$$

Divide -\frac{5}{12}, the coefficient of the x term, by 2 to get -\frac{5}{24}. Then add the square of -\frac{5}{24} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-\frac{5}{12}x+\left(-\frac{5}{24}\right)^{2}=\left(-\frac{5}{24}\right)^{2}$$

Square -\frac{5}{24} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-\frac{5}{12}x+\frac{25}{576}=\frac{25}{576}$$

Factor x^{2}-\frac{5}{12}x+\frac{25}{576}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{5}{24}\right)^{2}=\frac{25}{576}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{5}{24}\right)^{2}}=\sqrt{\frac{25}{576}}$$

Simplify.

$$x-\frac{5}{24}=\frac{5}{24} x-\frac{5}{24}=-\frac{5}{24}$$

Add \frac{5}{24} to both sides of the equation.

$$x=\frac{5}{12} x=0$$