Solve for x 49^(2x^2+3)=343^(x^2+5)

$49^{2 x^{2} + 3} = 343^{x^{2} + 5}$

Step 1

Create equivalent expressions in the equation that all have equal bases.

$7^{2 (2 x^{2} + 3)} = 7^{3 (x^{2} + 5)}$

Step 2

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$2 (2 x^{2} + 3) = 3 (x^{2} + 5)$

Step 3

Solve for $x$ .

Simplify $2 (2 x^{2} + 3)$ .

Start simplifying.

$0 + 0 + 2 (2 x^{2} + 3) = 3 (x^{2} + 5)$

Simplify by adding zeros.

$2 (2 x^{2} + 3) = 3 (x^{2} + 5)$

Apply the distributive property.

$2 (2 x^{2}) + 2 \cdot 3 = 3 (x^{2} + 5)$

Multiply.

Multiply $2$ by $2$ .

$4 x^{2} + 2 \cdot 3 = 3 (x^{2} + 5)$

Multiply $2$ by $3$ .

$4 x^{2} + 6 = 3 (x^{2} + 5)$

Simplify $3 (x^{2} + 5)$ .

Apply the distributive property.

$4 x^{2} + 6 = 3 x^{2} + 3 \cdot 5$

Multiply $3$ by $5$ .

$4 x^{2} + 6 = 3 x^{2} + 15$

Move all terms containing $x$ to the left side of the equation.

Subtract $3 x^{2}$ from both sides of the equation.

$4 x^{2} + 6 - 3 x^{2} = 15$

Subtract $3 x^{2}$ from $4 x^{2}$ .

$x^{2} + 6 = 15$

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

Subtract $6$ from both sides of the equation.

$x^{2} = 15 - 6$

Subtract $6$ from $15$ .

$x^{2} = 9$

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

$x = \pm \sqrt{9}$

Simplify $\pm \sqrt{9}$ .

Rewrite $9$ as $3^{2}$ .

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

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 3$

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.

$x = 3$

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

$x = - 3$

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

$x = 3, - 3$

Solve for x 49^(2x^2+3)=343^(x^2+5)

Related Questions

Support LCMGCF.com by disabling your adblocker.