Solve by Factoring 4x^2-50x+49=50x

$4 x^{2} - 50 x + 49 = 50 x$

Step 1

Subtract $50 x$ from both sides of the equation.

$4 x^{2} - 50 x + 49 - 50 x = 0$

Step 2

Subtract $50 x$ from $- 50 x$ .

$4 x^{2} - 100 x + 49 = 0$

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 $a \cdot c = 4 \cdot 49 = 196$ and whose sum is $b = - 100$ .

Factor $- 100$ out of $- 100 x$ .

$4 x^{2} - 100 x + 49 = 0$

Rewrite $- 100$ as $- 2$ plus $- 98$

$4 x^{2} + (- 2 - 98) x + 49 = 0$

Apply the distributive property.

$4 x^{2} - 2 x - 98 x + 49 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(4 x^{2} - 2 x) - 98 x + 49 = 0$

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

$2 x (2 x - 1) - 49 (2 x - 1) = 0$

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

$(2 x - 1) (2 x - 49) = 0$

Step 4

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

$2 x - 1 = 0$

$2 x - 49 = 0$

Step 5

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 6

Set $2 x - 49$ equal to $0$ and solve for $x$ .

Set $2 x - 49$ equal to $0$ .

$2 x - 49 = 0$

Solve $2 x - 49 = 0$ for $x$ .

Add $49$ to both sides of the equation.

$2 x = 49$

Divide each term in $2 x = 49$ by $2$ and simplify.

Divide each term in $2 x = 49$ by $2$ .

$\frac{2 x}{2} = \frac{49}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{49}{2}$

Divide $x$ by $1$ .

$x = \frac{49}{2}$

Step 7

The final solution is all the values that make $(2 x - 1) (2 x - 49) = 0$ true.

$x = \frac{1}{2}, \frac{49}{2}$

Solve by Factoring 4x^2-50x+49=50x

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