Solve Using the Quadratic Formula 3x^2-25=29

$3 x^{2} - 25 = 29$

Step 1

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

Subtract $29$ from both sides of the equation.

$3 x^{2} - 25 - 29 = 0$

Subtract $29$ from $- 25$ .

$3 x^{2} - 54 = 0$

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 $a = 3$ , $b = 0$ , and $c = - 54$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (3 \cdot - 54)}}{2 \cdot 3}$

Step 4

Simplify.

Simplify the numerator.

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

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 3 \cdot - 54}}{2 \cdot 3}$

Multiply $- 4 \cdot 3 \cdot - 54$ .

Multiply $- 4$ by $3$ .

$x = \frac{0 \pm \sqrt{0 - 12 \cdot - 54}}{2 \cdot 3}$

Multiply $- 12$ by $- 54$ .

$x = \frac{0 \pm \sqrt{0 + 648}}{2 \cdot 3}$

Add $0$ and $648$ .

$x = \frac{0 \pm \sqrt{648}}{2 \cdot 3}$

Rewrite $648$ as $18^{2} \cdot 2$ .

Factor $324$ out of $648$ .

$x = \frac{0 \pm \sqrt{324 (2)}}{2 \cdot 3}$

Rewrite $324$ as $18^{2}$ .

$x = \frac{0 \pm \sqrt{18^{2} \cdot 2}}{2 \cdot 3}$

Pull terms out from under the radical.

$x = \frac{0 \pm 18 \sqrt{2}}{2 \cdot 3}$

Multiply $2$ by $3$ .

$x = \frac{0 \pm 18 \sqrt{2}}{6}$

Simplify $\frac{0 \pm 18 \sqrt{2}}{6}$ .

$x = \pm 3 \sqrt{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \pm 3 \sqrt{2}$

Decimal Form:

$x = 4.24264068 \dots, - 4.24264068 \dots$