Solve for m 4m^2+8m-4=1

$4 m^{2} + 8 m - 4 = 1$

Step 1

Subtract $1$ from both sides of the equation.

$4 m^{2} + 8 m - 4 - 1 = 0$

Step 2

Subtract $1$ from $- 4$ .

$4 m^{2} + 8 m - 5 = 0$

Step 3

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 $a \cdot c = 4 \cdot - 5 = - 20$ and whose sum is $b = 8$ .

Factor $8$ out of $8 m$ .

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

Rewrite $8$ as $- 2$ plus $10$

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

Apply the distributive property.

$4 m^{2} - 2 m + 10 m - 5 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

$2 m (2 m - 1) + 5 (2 m - 1) = 0$

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

$(2 m - 1) (2 m + 5) = 0$

Step 4

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

$2 m - 1 = 0$

$2 m + 5 = 0$

Step 5

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

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

$2 m - 1 = 0$

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

Add $1$ to both sides of the equation.

$2 m = 1$

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

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

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $m$ by $1$ .

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

Step 6

Set $2 m + 5$ equal to $0$ and solve for $m$ .

Set $2 m + 5$ equal to $0$ .

$2 m + 5 = 0$

Solve $2 m + 5 = 0$ for $m$ .

Subtract $5$ from both sides of the equation.

$2 m = - 5$

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

Divide each term in $2 m = - 5$ by $2$ .

$\frac{2 m}{2} = \frac{- 5}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 m}{2} = \frac{- 5}{2}$

Divide $m$ by $1$ .

$m = \frac{- 5}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$m = - \frac{5}{2}$

Step 7

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

$m = \frac{1}{2}, - \frac{5}{2}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$m = \frac{1}{2}, - \frac{5}{2}$

Decimal Form:

$m = 0.5, - 2.5$

Mixed Number Form:

$m = \frac{1}{2}, - 2 \frac{1}{2}$

Solve for m 4m^2+8m-4=1

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