Solve Using the Quadratic Formula x^2=4-7x

$x^{2} = 4 - 7 x$

Step 1

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

Subtract $4$ from both sides of the equation.

$x^{2} - 4 = - 7 x$

Add $7 x$ to both sides of the equation.

$x^{2} - 4 + 7 x = 0$

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 $a = 1$ , $b = 7$ , and $c = - 4$ into the quadratic formula and solve for $x$ .

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

Step 4

Simplify.

Simplify the numerator.

Raise $7$ to the power of $2$ .

$x = \frac{- 7 \pm \sqrt{49 - 4 \cdot 1 \cdot - 4}}{2 \cdot 1}$

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

Multiply $- 4$ by $1$ .

$x = \frac{- 7 \pm \sqrt{49 - 4 \cdot - 4}}{2 \cdot 1}$

Multiply $- 4$ by $- 4$ .

$x = \frac{- 7 \pm \sqrt{49 + 16}}{2 \cdot 1}$

Add $49$ and $16$ .

$x = \frac{- 7 \pm \sqrt{65}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 7 \pm \sqrt{65}}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{- 7 \pm \sqrt{65}}{2}$

Decimal Form:

$x = 0.53112887 \dots, - 7.53112887 \dots$