Solve Using the Quadratic Formula 5(x^2-6)+5=5

$5 (x^{2} - 6) + 5 = 5$

Step 1

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

Simplify the left side.

Simplify $5 (x^{2} - 6) + 5$ .

Simplify each term.

Apply the distributive property.

$5 x^{2} + 5 \cdot - 6 + 5 = 5$

Multiply $5$ by $- 6$ .

$5 x^{2} - 30 + 5 = 5$

Add $- 30$ and $5$ .

$5 x^{2} - 25 = 5$

Subtract $5$ from both sides of the equation.

$5 x^{2} - 25 - 5 = 0$

Subtract $5$ from $- 25$ .

$5 x^{2} - 30 = 0$

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 $a = 5$ , $b = 0$ , and $c = - 30$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (5 \cdot - 30)}}{2 \cdot 5}$

Step 4

Simplify.

Simplify the numerator.

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

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 5 \cdot - 30}}{2 \cdot 5}$

Multiply $- 4 \cdot 5 \cdot - 30$ .

Multiply $- 4$ by $5$ .

$x = \frac{0 \pm \sqrt{0 - 20 \cdot - 30}}{2 \cdot 5}$

Multiply $- 20$ by $- 30$ .

$x = \frac{0 \pm \sqrt{0 + 600}}{2 \cdot 5}$

Add $0$ and $600$ .

$x = \frac{0 \pm \sqrt{600}}{2 \cdot 5}$

Rewrite $600$ as $10^{2} \cdot 6$ .

Factor $100$ out of $600$ .

$x = \frac{0 \pm \sqrt{100 (6)}}{2 \cdot 5}$

Rewrite $100$ as $10^{2}$ .

$x = \frac{0 \pm \sqrt{10^{2} \cdot 6}}{2 \cdot 5}$

Pull terms out from under the radical.

$x = \frac{0 \pm 10 \sqrt{6}}{2 \cdot 5}$

Multiply $2$ by $5$ .

$x = \frac{0 \pm 10 \sqrt{6}}{10}$

Simplify $\frac{0 \pm 10 \sqrt{6}}{10}$ .

$x = \pm \sqrt{6}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \pm \sqrt{6}$

Decimal Form:

$x = 2.44948974 \dots, - 2.44948974 \dots$

Solve Using the Quadratic Formula 5(x^2-6)+5=5

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