Question

The area of the rectangle is 90 square feet. Find $x$.

Short answer

The values of $x=-9,10$.

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. Write the standard form of a quadratic equation.

The standard form of a quadratic equation is given by

$a{x}^2+bx+c=0$, where$a\ne 0$

Step 3. Define the area of the rectangle.

$\mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{rectangle}=\mathrm{length}\times \mathrm{width}\dots \dots \dots ..\left(1\right)$

Step 4. Find the value of x for the given rectangle.

Observe the figure.

The length of the rectangle$=\left(x-1\right)$ feet

The width of the rectangle$=x$ feet

The area of the rectangle $=90$square feet

Use equation (1).

role="math" localid="1647949732123" $$\begin{gathered} \left(x-1\right)\left(x\right)=90 \\ {x}^2-x=90 \\ {x}^2-x-90=0 \\ {x}^2-10x+9x-90=0 \\ x\left(x-10\right)+9\left(x-10\right)=0 \\ \left(x-10\right)\left(x+9\right)=0 \\ x=-9,10 \end{gathered}$$

Therefore the values of $x=-9,10$.