Solve over the Interval 7x(x^2-1)=100 , (-3,30)

$7 x (x^{2} - 1) = 100$ , $(- 3, 30)$

Step 1

Simplify $7 x (x^{2} - 1)$ .

Apply the distributive property.

$7 x \cdot x^{2} + 7 x \cdot - 1 = 100$

Multiply $x$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$7 (x^{2} x) + 7 x \cdot - 1 = 100$

Multiply $x^{2}$ by $x$ .

Raise $x$ to the power of $1$ .

$7 (x^{2} x^{1}) + 7 x \cdot - 1 = 100$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$7 x^{2 + 1} + 7 x \cdot - 1 = 100$

Add $2$ and $1$ .

$7 x^{3} + 7 x \cdot - 1 = 100$

Multiply $- 1$ by $7$ .

$7 x^{3} - 7 x = 100$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x \approx 2.56366517$

Step 3

The interval $(- 3, 30)$ contains $2.56366517$ .

$x = 2.56366517$

Step 4