Question

Solve the given equation.

$\mathbf{2}\left(4w+w^2\right)\mathbf{-}\mathbf{6}\mathbf{=}\mathbf{2}\mathit{w}\left(w-4\right)\mathbf{+}\mathbf{10}$

Short answer

$\mathit{w}\mathbf{=}\mathbf{1}$ is the solution of the given equation.

Step-by-step solution

Step 1. Define an equation.

In mathematics, an equation is a statement that asserts the equality of two expressions, which are connected by the equal sign $"="$.

Step 2. Define the power of a product rule.

Power of a product rule states that if the two exponents of the same base are multiplied then the exponents are added and base remains the same.

$a^m.a^n=a^{m+n}$

Where,$a$ is any non-zero real number.

Step 3. Solve the equation, 2(4w+w2)−6=2w(w−4)+10.

Use the power of a product rule to solve the equation.

$\begin{array}{c}2\left(4w+w^2\right)-6=2w\left(w-4\right)+10\\ 2\left(4w\right)+2\left(w^2\right)-6=2w\left(w\right)-2w\left(4\right)+10\\ {\text{8w+2w}}^2-6=2w^2-8w+10\\ {\text{8w+2w}}^2-2w^2+8w=10+6\\ 16w=16\\ w=\frac{16}{16}\\ w=1\end{array}$

Therefore,$w=1$ is the solution of the given equation.