Solve Using the Quadratic Formula -2x(5x-2)=0

$- 2 x (5 x - 2) = 0$

Step 1

Simplify the left side.

Simplify $- 2 x (5 x - 2)$ .

Simplify by multiplying through.

Apply the distributive property.

$- 2 x (5 x) - 2 x \cdot - 2 = 0$

Simplify the expression.

Rewrite using the commutative property of multiplication.

$- 2 \cdot 5 x \cdot x - 2 x \cdot - 2 = 0$

Multiply $- 2$ by $- 2$ .

$- 2 \cdot 5 x \cdot x + 4 x = 0$

Simplify each term.

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$- 2 \cdot 5 (x \cdot x) + 4 x = 0$

Multiply $x$ by $x$ .

$- 2 \cdot 5 x^{2} + 4 x = 0$

Multiply $- 2$ by $5$ .

$- 10 x^{2} + 4 x = 0$

Step 2

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

Substitute the values $a = - 10$ , $b = 4$ , and $c = 0$ into the quadratic formula and solve for $x$ .

$\frac{- 4 \pm \sqrt{4^{2} - 4 \cdot (- 10 \cdot 0)}}{2 \cdot - 10}$

Step 4

Simplify.

Simplify the numerator.

Raise $4$ to the power of $2$ .

$x = \frac{- 4 \pm \sqrt{16 - 4 \cdot - 10 \cdot 0}}{2 \cdot - 10}$

Multiply $- 4 \cdot - 10 \cdot 0$ .

Multiply $- 4$ by $- 10$ .

$x = \frac{- 4 \pm \sqrt{16 + 40 \cdot 0}}{2 \cdot - 10}$

Multiply $40$ by $0$ .

$x = \frac{- 4 \pm \sqrt{16 + 0}}{2 \cdot - 10}$

Add $16$ and $0$ .

$x = \frac{- 4 \pm \sqrt{16}}{2 \cdot - 10}$

Rewrite $16$ as $4^{2}$ .

$x = \frac{- 4 \pm \sqrt{4^{2}}}{2 \cdot - 10}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \frac{- 4 \pm 4}{2 \cdot - 10}$

Multiply $2$ by $- 10$ .

$x = \frac{- 4 \pm 4}{- 20}$

Simplify $\frac{- 4 \pm 4}{- 20}$ .

$x = \frac{1 \pm 1}{5}$

Step 5

The final answer is the combination of both solutions.

$x = \frac{2}{5}, 0$

Solve Using the Quadratic Formula -2x(5x-2)=0

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