Solve for x -10x^2+13x=4

$- 10 x^{2} + 13 x = 4$

Step 1

Subtract $4$ from both sides of the equation.

$- 10 x^{2} + 13 x - 4 = 0$

Step 2

Factor the left side of the equation.

Factor $- 1$ out of $- 10 x^{2} + 13 x - 4$ .

Factor $- 1$ out of $- 10 x^{2}$ .

$- (10 x^{2}) + 13 x - 4 = 0$

Factor $- 1$ out of $13 x$ .

$- (10 x^{2}) - (- 13 x) - 4 = 0$

Rewrite $- 4$ as $- 1 (4)$ .

$- (10 x^{2}) - (- 13 x) - 1 \cdot 4 = 0$

Factor $- 1$ out of $- (10 x^{2}) - (- 13 x)$ .

$- (10 x^{2} - 13 x) - 1 \cdot 4 = 0$

Factor $- 1$ out of $- (10 x^{2} - 13 x) - 1 (4)$ .

$- (10 x^{2} - 13 x + 4) = 0$

Factor.

Factor by grouping.

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 10 \cdot 4 = 40$ and whose sum is $b = - 13$ .

Factor $- 13$ out of $- 13 x$ .

$- (10 x^{2} - 13 x + 4) = 0$

Rewrite $- 13$ as $- 5$ plus $- 8$

$- (10 x^{2} + (- 5 - 8) x + 4) = 0$

Apply the distributive property.

$- (10 x^{2} - 5 x - 8 x + 4) = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$- ((10 x^{2} - 5 x) - 8 x + 4) = 0$

Factor out the greatest common factor (GCF) from each group.

$- (5 x (2 x - 1) - 4 (2 x - 1)) = 0$

Factor the polynomial by factoring out the greatest common factor, $2 x - 1$ .

$- ((2 x - 1) (5 x - 4)) = 0$

Remove unnecessary parentheses.

$- (2 x - 1) (5 x - 4) = 0$

Step 3

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$2 x - 1 = 0$

$5 x - 4 = 0$

Step 4

Set $2 x - 1$ equal to $0$ and solve for $x$ .

Set $2 x - 1$ equal to $0$ .

$2 x - 1 = 0$

Solve $2 x - 1 = 0$ for $x$ .

Add $1$ to both sides of the equation.

$2 x = 1$

Divide each term in $2 x = 1$ by $2$ and simplify.

Divide each term in $2 x = 1$ by $2$ .

$\frac{2 x}{2} = \frac{1}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{1}{2}$

Divide $x$ by $1$ .

$x = \frac{1}{2}$

Step 5

Set $5 x - 4$ equal to $0$ and solve for $x$ .

Set $5 x - 4$ equal to $0$ .

$5 x - 4 = 0$

Solve $5 x - 4 = 0$ for $x$ .

Add $4$ to both sides of the equation.

$5 x = 4$

Divide each term in $5 x = 4$ by $5$ and simplify.

Divide each term in $5 x = 4$ by $5$ .

$\frac{5 x}{5} = \frac{4}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{4}{5}$

Divide $x$ by $1$ .

$x = \frac{4}{5}$

Step 6

The final solution is all the values that make $- (2 x - 1) (5 x - 4) = 0$ true.

$x = \frac{1}{2}, \frac{4}{5}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{2}, \frac{4}{5}$

Decimal Form:

$x = 0.5, 0.8$

Solve for x -10x^2+13x=4

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