Solve for x 7x^2+4x-3=0

$7 x^{2} + 4 x - 3 = 0$

Step 1

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 $a \cdot c = 7 \cdot - 3 = - 21$ and whose sum is $b = 4$ .

Factor $4$ out of $4 x$ .

$7 x^{2} + 4 (x) - 3 = 0$

Rewrite $4$ as $- 3$ plus $7$

$7 x^{2} + (- 3 + 7) x - 3 = 0$

Apply the distributive property.

$7 x^{2} - 3 x + 7 x - 3 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(7 x^{2} - 3 x) + 7 x - 3 = 0$

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

$x (7 x - 3) + 1 (7 x - 3) = 0$

Factor the polynomial by factoring out the greatest common factor, $7 x - 3$ .

$(7 x - 3) (x + 1) = 0$

Step 2

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

$7 x - 3 = 0$

$x + 1 = 0$

Step 3

Set $7 x - 3$ equal to $0$ and solve for $x$ .

Set $7 x - 3$ equal to $0$ .

$7 x - 3 = 0$

Solve $7 x - 3 = 0$ for $x$ .

Add $3$ to both sides of the equation.

$7 x = 3$

Divide each term in $7 x = 3$ by $7$ and simplify.

Divide each term in $7 x = 3$ by $7$ .

$\frac{7 x}{7} = \frac{3}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{3}{7}$

Divide $x$ by $1$ .

$x = \frac{3}{7}$

Step 4

Set $x + 1$ equal to $0$ and solve for $x$ .

Set $x + 1$ equal to $0$ .

$x + 1 = 0$

Subtract $1$ from both sides of the equation.

$x = - 1$

Step 5

The final solution is all the values that make $(7 x - 3) (x + 1) = 0$ true.

$x = \frac{3}{7}, - 1$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{3}{7}, - 1$

Decimal Form:

$x = 0.\overline{428571}, - 1$

Solve for x 7x^2+4x-3=0

Related Questions

Support LCMGCF.com by disabling your adblocker.