Finite Math Examples

$e^{2 x} \cdot (2 x - 1) - 1 = 0$

Step 1

Simplify $e^{2 x} \cdot (2 x - 1) - 1$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$e^{2 x} (2 x) + e^{2 x} \cdot - 1 - 1 = 0$

Step 1.1.2

Rewrite using the commutative property of multiplication.

$2 e^{2 x} x + e^{2 x} \cdot - 1 - 1 = 0$

Step 1.1.3

Move $- 1$ to the left of $e^{2 x}$ .

$2 e^{2 x} x - 1 \cdot e^{2 x} - 1 = 0$

Step 1.1.4

Rewrite $- 1 e^{2 x}$ as $- e^{2 x}$ .

$2 e^{2 x} x - e^{2 x} - 1 = 0$

Step 1.2

Reorder factors in $2 e^{2 x} x - e^{2 x} - 1$ .

$2 x e^{2 x} - e^{2 x} - 1 = 0$

Step 2

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

$x \approx 0.63923227$

Step 3