Solve Using the Square Root Property 4x^2-6=74

$4 x^{2} - 6 = 74$

Step 1

Move all terms not containing $x$ to the right side of the equation.

Add $6$ to both sides of the equation.

$4 x^{2} = 74 + 6$

Add $74$ and $6$ .

$4 x^{2} = 80$

Step 2

Divide each term in $4 x^{2} = 80$ by $4$ and simplify.

Divide each term in $4 x^{2} = 80$ by $4$ .

$\frac{4 x^{2}}{4} = \frac{80}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x^{2}}{4} = \frac{80}{4}$

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{80}{4}$

Simplify the right side.

Divide $80$ by $4$ .

$x^{2} = 20$

Step 3

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{20}$

Step 4

Simplify $\pm \sqrt{20}$ .

Rewrite $20$ as $2^{2} \cdot 5$ .

Factor $4$ out of $20$ .

$x = \pm \sqrt{4 (5)}$

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

$x = \pm \sqrt{2^{2} \cdot 5}$

Pull terms out from under the radical.

$x = \pm 2 \sqrt{5}$

Step 5

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = 2 \sqrt{5}$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 2 \sqrt{5}$

The complete solution is the result of both the positive and negative portions of the solution.

$x = 2 \sqrt{5}, - 2 \sqrt{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = 2 \sqrt{5}, - 2 \sqrt{5}$

Decimal Form:

$x = 4.47213595 \dots, - 4.47213595 \dots$

Solve Using the Square Root Property 4x^2-6=74

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