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

$4 = x^{2} - 7$

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

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

Add $7$ to both sides of the equation.

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

Add $4$ and $7$ .

$- x^{2} + 11 = 0$

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 $a = - 1$ , $b = 0$ , and $c = 11$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (- 1 \cdot 11)}}{2 \cdot - 1}$

Step 4

Simplify.

Simplify the numerator.

Raising $0$ to any positive power yields $0$ .

$x = \frac{0 \pm \sqrt{0 - 4 \cdot - 1 \cdot 11}}{2 \cdot - 1}$

Multiply $- 4 \cdot - 1 \cdot 11$ .

Multiply $- 4$ by $- 1$ .

$x = \frac{0 \pm \sqrt{0 + 4 \cdot 11}}{2 \cdot - 1}$

Multiply $4$ by $11$ .

$x = \frac{0 \pm \sqrt{0 + 44}}{2 \cdot - 1}$

Add $0$ and $44$ .

$x = \frac{0 \pm \sqrt{44}}{2 \cdot - 1}$

Rewrite $44$ as $2^{2} \cdot 11$ .

Factor $4$ out of $44$ .

$x = \frac{0 \pm \sqrt{4 (11)}}{2 \cdot - 1}$

Rewrite $4$ as $2^{2}$ .

$x = \frac{0 \pm \sqrt{2^{2} \cdot 11}}{2 \cdot - 1}$

Pull terms out from under the radical.

$x = \frac{0 \pm 2 \sqrt{11}}{2 \cdot - 1}$

Multiply $2$ by $- 1$ .

$x = \frac{0 \pm 2 \sqrt{11}}{- 2}$

Simplify $\frac{0 \pm 2 \sqrt{11}}{- 2}$ .

$x = \pm \sqrt{11}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \pm \sqrt{11}$

Decimal Form:

$x = 3.31662479 \dots, - 3.31662479 \dots$