Solve Using the Quadratic Formula x^2+12x=7x+1

$x^{2} + 12 x = 7 x + 1$

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

Move all the expressions to the left side of the equation.

Subtract $7 x$ from both sides of the equation.

$x^{2} + 12 x - 7 x = 1$

Subtract $1$ from both sides of the equation.

$x^{2} + 12 x - 7 x - 1 = 0$

Subtract $7 x$ from $12 x$ .

$x^{2} + 5 x - 1 = 0$

Use the quadratic formula to find the solutions.

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

Substitute the values $a = 1$ , $b = 5$ , and $c = - 1$ into the quadratic formula and solve for $x$ .

$\frac{- 5 \pm \sqrt{5^{2} - 4 \cdot (1 \cdot - 1)}}{2 \cdot 1}$

Simplify.

Simplify the numerator.

Raise $5$ to the power of $2$ .

$x = \frac{- 5 \pm \sqrt{25 - 4 \cdot 1 \cdot - 1}}{2 \cdot 1}$

Multiply $- 4$ by $1$ .

$x = \frac{- 5 \pm \sqrt{25 - 4 \cdot - 1}}{2 \cdot 1}$

Multiply $- 4$ by $- 1$ .

$x = \frac{- 5 \pm \sqrt{25 + 4}}{2 \cdot 1}$

Add $25$ and $4$ .

$x = \frac{- 5 \pm \sqrt{29}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 5 \pm \sqrt{29}}{2}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{- 5 \pm \sqrt{29}}{2}$

Decimal Form:

$x = 0.19258240 \dots, - 5.19258240 \dots$