Solve Using the Quadratic Formula 2x^2-13x+7=x^2

$2 x^{2} - 13 x + 7 = x^{2}$

Step 1

Move all terms to the left side of the equation and simplify.

Subtract $x^{2}$ from both sides of the equation.

$2 x^{2} - 13 x + 7 - x^{2} = 0$

Subtract $x^{2}$ from $2 x^{2}$ .

$x^{2} - 13 x + 7 = 0$

Step 2

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

Substitute the values $a = 1$ , $b = - 13$ , and $c = 7$ into the quadratic formula and solve for $x$ .

$\frac{13 \pm \sqrt{{(- 13)}^{2} - 4 \cdot (1 \cdot 7)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 13$ to the power of $2$ .

$x = \frac{13 \pm \sqrt{169 - 4 \cdot 1 \cdot 7}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 7$ .

Multiply $- 4$ by $1$ .

$x = \frac{13 \pm \sqrt{169 - 4 \cdot 7}}{2 \cdot 1}$

Multiply $- 4$ by $7$ .

$x = \frac{13 \pm \sqrt{169 - 28}}{2 \cdot 1}$

Subtract $28$ from $169$ .

$x = \frac{13 \pm \sqrt{141}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{13 \pm \sqrt{141}}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{13 \pm \sqrt{141}}{2}$

Decimal Form:

$x = 12.43717104 \dots, 0.56282895 \dots$