Question

solve the equation. round your answer to two decimal places when necessary

1. \\(7x^3 = 3584\\)
2. \\(x^4 - 10 = 6551\\)
3. \\((x + 3)^7 = -78125\\)

Explanation:

Problem 13:

Step1: Isolate $x^3$ term

Divide both sides by 7:
$\frac{7x^3}{7} = \frac{3584}{7}$
$x^3 = 512$

Step2: Solve for $x$

Take cube root of both sides:
$x = \sqrt[3]{512}$
$x = 8$

Problem 14:

Step1: Isolate $x^4$ term

Add 10 to both sides:
$x^4 - 10 + 10 = 6551 + 10$
$x^4 = 6561$

Step2: Solve for $x$

Take 4th root of both sides (note: 4th root of positive number has positive and negative solutions):
$x = \pm\sqrt[4]{6561}$
$x = \pm9$

Problem 15:

Step1: Isolate $(x+3)$ term

Take 7th root of both sides (7th root preserves negative sign):
$x+3 = \sqrt[7]{-78125}$
$x+3 = -5$

Step2: Solve for $x$

Subtract 3 from both sides:
$x + 3 - 3 = -5 - 3$
$x = -8$

Answer:

1. $x = 8$
2. $x = 9$ and $x = -9$
3. $x = -8$