Solve for x 64^(12x+81)=8^(3x^2+15x)

$64^{12 x + 81} = 8^{3 x^{2} + 15 x}$

Step 1

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

$8^{2 (12 x + 81)} = 8^{3 x^{2} + 15 x}$

Step 2

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

$2 (12 x + 81) = 3 x^{2} + 15 x$

Step 3

Solve for $x$ .

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$3 x^{2} + 15 x = 2 (12 x + 81)$

Simplify $2 (12 x + 81)$ .

Apply the distributive property.

$3 x^{2} + 15 x = 2 (12 x) + 2 \cdot 81$

Multiply.

Multiply $12$ by $2$ .

$3 x^{2} + 15 x = 24 x + 2 \cdot 81$

Multiply $2$ by $81$ .

$3 x^{2} + 15 x = 24 x + 162$

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

Subtract $24 x$ from both sides of the equation.

$3 x^{2} + 15 x - 24 x = 162$

Subtract $24 x$ from $15 x$ .

$3 x^{2} - 9 x = 162$

Subtract $162$ from both sides of the equation.

$3 x^{2} - 9 x - 162 = 0$

Factor the left side of the equation.

Factor $3$ out of $3 x^{2} - 9 x - 162$ .

Factor $3$ out of $3 x^{2}$ .

$3 (x^{2}) - 9 x - 162 = 0$

Factor $3$ out of $- 9 x$ .

$3 (x^{2}) + 3 (- 3 x) - 162 = 0$

Factor $3$ out of $- 162$ .

$3 x^{2} + 3 (- 3 x) + 3 \cdot - 54 = 0$

Factor $3$ out of $3 x^{2} + 3 (- 3 x)$ .

$3 (x^{2} - 3 x) + 3 \cdot - 54 = 0$

Factor $3$ out of $3 (x^{2} - 3 x) + 3 \cdot - 54$ .

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

Factor.

Factor $x^{2} - 3 x - 54$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 54$ and whose sum is $- 3$ .

$- 9, 6$

Write the factored form using these integers.

$3 ((x - 9) (x + 6)) = 0$

Remove unnecessary parentheses.

$3 (x - 9) (x + 6) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x - 9 = 0$

$x + 6 = 0$

Set $x - 9$ equal to $0$ and solve for $x$ .

Set $x - 9$ equal to $0$ .

$x - 9 = 0$

Add $9$ to both sides of the equation.

$x = 9$

Set $x + 6$ equal to $0$ and solve for $x$ .

Set $x + 6$ equal to $0$ .

$x + 6 = 0$

Subtract $6$ from both sides of the equation.

$x = - 6$

The final solution is all the values that make $3 (x - 9) (x + 6) = 0$ true.

$x = 9, - 6$

Solve for x 64^(12x+81)=8^(3x^2+15x)

Related Questions

Support LCMGCF.com by disabling your adblocker.