Solve for x 2x^2-28x=-98

$2 x^{2} - 28 x = - 98$

Step 1

Add $98$ to both sides of the equation.

$2 x^{2} - 28 x + 98 = 0$

Step 2

Factor the left side of the equation.

Factor $2$ out of $2 x^{2} - 28 x + 98$ .

Factor $2$ out of $2 x^{2}$ .

$2 (x^{2}) - 28 x + 98 = 0$

Factor $2$ out of $- 28 x$ .

$2 (x^{2}) + 2 (- 14 x) + 98 = 0$

Factor $2$ out of $98$ .

$2 x^{2} + 2 (- 14 x) + 2 \cdot 49 = 0$

Factor $2$ out of $2 x^{2} + 2 (- 14 x)$ .

$2 (x^{2} - 14 x) + 2 \cdot 49 = 0$

Factor $2$ out of $2 (x^{2} - 14 x) + 2 \cdot 49$ .

$2 (x^{2} - 14 x + 49) = 0$

Factor using the perfect square rule.

Rewrite $49$ as $7^{2}$ .

$2 (x^{2} - 14 x + 7^{2}) = 0$

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

$14 x = 2 \cdot x \cdot 7$

Rewrite the polynomial.

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

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = x$ and $b = 7$ .

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

Step 3

Divide each term in $2 {(x - 7)}^{2} = 0$ by $2$ and simplify.

Divide each term in $2 {(x - 7)}^{2} = 0$ by $2$ .

$\frac{2 {(x - 7)}^{2}}{2} = \frac{0}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 {(x - 7)}^{2}}{2} = \frac{0}{2}$

Divide ${(x - 7)}^{2}$ by $1$ .

${(x - 7)}^{2} = \frac{0}{2}$

Simplify the right side.

Divide $0$ by $2$ .

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

Step 4

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

$x - 7 = 0$

Step 5

Add $7$ to both sides of the equation.

$x = 7$