Solve (x/5+4/5)*x/2=3.2

$$( \frac { x } { 5 } + \frac { 4 } { 5 } ) \times \frac { x } { 2 } = 3.2$$

Solve for x

$$x=-8$$

$$x=4$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 10, the least common multiple of 5,2.

$$5\left(\frac{x}{5}+\frac{4}{5}\right)x=32$$

Since \frac{x}{5} and \frac{4}{5} have the same denominator, add them by adding their numerators.

$$5\times \frac{x+4}{5}x=32$$

Express 5\times \frac{x+4}{5} as a single fraction.

$$\frac{5\left(x+4\right)}{5}x=32$$

Cancel out 5 and 5.

$$\left(x+4\right)x=32$$

Use the distributive property to multiply x+4 by x.

$$x^{2}+4x=32$$

Subtract 32 from both sides.

$$x^{2}+4x-32=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 4 for b, and -32 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-4±\sqrt{4^{2}-4\left(-32\right)}}{2}$$

Square 4.

$$x=\frac{-4±\sqrt{16-4\left(-32\right)}}{2}$$

Multiply -4 times -32.

$$x=\frac{-4±\sqrt{16+128}}{2}$$

Add 16 to 128.

$$x=\frac{-4±\sqrt{144}}{2}$$

Take the square root of 144.

$$x=\frac{-4±12}{2}$$

Now solve the equation x=\frac{-4±12}{2} when ± is plus. Add -4 to 12.

$$x=\frac{8}{2}$$

Divide 8 by 2.

$$x=4$$

Now solve the equation x=\frac{-4±12}{2} when ± is minus. Subtract 12 from -4.

$$x=-\frac{16}{2}$$

Divide -16 by 2.

$$x=-8$$

The equation is now solved.

$$x=4 x=-8$$

Steps for Completing the Square

Multiply both sides of the equation by 10, the least common multiple of 5,2.

$$5\left(\frac{x}{5}+\frac{4}{5}\right)x=32$$

Since \frac{x}{5} and \frac{4}{5} have the same denominator, add them by adding their numerators.

$$5\times \frac{x+4}{5}x=32$$

Express 5\times \frac{x+4}{5} as a single fraction.

$$\frac{5\left(x+4\right)}{5}x=32$$

Cancel out 5 and 5.

$$\left(x+4\right)x=32$$

Use the distributive property to multiply x+4 by x.

$$x^{2}+4x=32$$

Divide 4, the coefficient of the x term, by 2 to get 2. Then add the square of 2 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+4x+2^{2}=32+2^{2}$$

Square 2.

$$x^{2}+4x+4=32+4$$

Add 32 to 4.

$$x^{2}+4x+4=36$$

Factor x^{2}+4x+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}.

$$\left(x+2\right)^{2}=36$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+2\right)^{2}}=\sqrt{36}$$

Simplify.

$$x+2=6 x+2=-6$$

Subtract 2 from both sides of the equation.

$$x=4 x=-8$$