How do you solve x^2 – 3x = 7x – 2 using the quadratic formula?

Jul 17, 2015

$x = 5 + \sqrt{23} , x = 5 - \sqrt{23}$

Explanation:

${x}^{2} - 3 x = 7 x - 2$

Get all of the terms on the left side.

${x}^{2} - 3 x - 7 x + 2 = 0$ =

${x}^{2} - 10 x + 2 = 0$

The equation is now in the form of a quadratic equation $a {x}^{2} + b x + c$, where $a = 1 ,$ $b = - 10 ,$ and $c = 2$.

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

Substitute the values for $a , b , \mathmr{and} c$ into the formula.

$x = \frac{- \left(- 10\right) \pm \sqrt{- {10}^{2} - 4 \cdot 1 \cdot 2}}{2 \cdot 1}$ =

$x = \frac{10 \pm \sqrt{100 - 8}}{2}$ =

$x = \frac{10 \pm \sqrt{92}}{2}$

Simplify $\sqrt{92}$.

$\sqrt{92} = \sqrt{2 \times 2 \times 23}$ =

$\sqrt{92} = 2 \sqrt{23}$

Substitute $2 \sqrt{23}$ for $\sqrt{92}$.

$x = \frac{10 \pm 2 \sqrt{23}}{2}$

Simplify.

$x = 5 \pm \sqrt{23}$

Solve for $x$.

$x = 5 + \sqrt{23}$

$x = 5 - \sqrt{23}$