Find the dimensions of the prayer hall discussed in Section 4.1. (The breadth $x$ satisfies $2x^2 + x - 300 = 0$.)

Step 1: State the given quadratic equation

We are given a quadratic equation that represents the breadth $x$ of the prayer hall. We need to solve this equation to find the value of $x$.

Step 2: Compare with standard quadratic equation

To solve the quadratic equation, we first identify the coefficients $a$, $b$, and $c$ by comparing it with the standard form of a quadratic equation.

Step 3: Identify coefficients

From the given equation $2x^2 + x - 300 = 0$, we can see that $a=2$, $b=1$, and $c=-300$.

Step 4: Apply the quadratic formula

The quadratic formula is used to find the roots of a quadratic equation. We substitute the values of $a$, $b$, and $c$ into this formula.

Step 5: Substitute values into the formula

Substitute the identified coefficients $a=2$, $b=1$, and $c=-300$ into the quadratic formula.

Step 6: Simplify the expression under the square root

First, calculate the term inside the square root: $1^2 = 1$ and $4(2)(-300) = -2400$. Then, $1 - (-2400) = 1 + 2400 = 2401$. The denominator is $2(2) = 4$.

Step 7: Calculate the square root

The square root of 2401 is 49. This simplifies the expression further.

Step 8: Solve for x using both positive and negative roots

Now we have two possible values for $x$: one by taking the positive square root and one by taking the negative square root.

Step 9: Calculate the first possible value of x

For the first root, we use the positive sign. $(-1 + 49)$ gives $48$, and $48$ divided by $4$ equals $12$.

Step 10: Calculate the second possible value of x

For the second root, we use the negative sign. $(-1 - 49)$ gives $-50$, and $-50$ divided by $4$ equals $-12.5$.

Step 11: Determine the valid breadth

Since $x$ represents the breadth of the prayer hall, it cannot be a negative value. Therefore, we discard $x = -12.5$ and take $x = 12$ metres as the breadth.

Step 12: Find the length of the hall

From Section 4.1 of the textbook, the length of the prayer hall is given as 'one metre more than twice its breadth', so Length $= 2x + 1$.

Step 13: Substitute the value of x to find the length

Substitute $x = 12$ metres into the expression for the length to calculate its value.

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