Solve for x 25x^2-20x-2=-6

$25 x^{2} - 20 x - 2 = - 6$

Step 1

Add $6$ to both sides of the equation.

$25 x^{2} - 20 x - 2 + 6 = 0$

Step 2

Add $- 2$ and $6$ .

$25 x^{2} - 20 x + 4 = 0$

Step 3

Factor using the perfect square rule.

Rewrite $25 x^{2}$ as ${(5 x)}^{2}$ .

${(5 x)}^{2} - 20 x + 4 = 0$

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

${(5 x)}^{2} - 20 x + 2^{2} = 0$

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$20 x = 2 \cdot (5 x) \cdot 2$

Rewrite the polynomial.

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

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = 5 x$ and $b = 2$ .

${(5 x - 2)}^{2} = 0$

Step 4

Set the $5 x - 2$ equal to $0$ .

$5 x - 2 = 0$

Step 5

Solve for $x$ .

Add $2$ to both sides of the equation.

$5 x = 2$

Divide each term in $5 x = 2$ by $5$ and simplify.

Divide each term in $5 x = 2$ by $5$ .

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

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0.4$