Brian is solving the equation x squared minus three-fourths x = 5. What value must be added to both sides of the equation to make the left side a perfect-square trinomial?

StartFraction 9 Over 64 EndFraction
StartFraction 9 Over 16 EndFraction
Three-fourths
Nine-fourths

We want to complete the square for the equation:

\[
x^2 - \frac{3}{4}x = 5
\]

To complete the square, we focus on the linear term \(- \frac{3}{4}x\). The steps are as follows:

1. Take half of the coefficient of \(x\), which is \(- \frac{3}{4}\).
   \[
   \frac{1}{2} \times - \frac{3}{4} = - \frac{3}{8}
   \]

2. Square this result:
   \[
   \left( - \frac{3}{8} \right)^2 = \frac{9}{64}
   \]

This value, \(\frac{9}{64}\), is what must be added to both sides of the equation to make the left side a perfect-square trinomial.

So the correct answer is:

\[
\boxed{\frac{9}{64}}
\]

---

Would you like further details on completing the square, or do you have any other questions? Here are some related questions:

1. How do you solve the complete equation after completing the square?
2. What is the general form of a perfect-square trinomial?
3. How does completing the square help in solving quadratic equations?
4. Can completing the square be used to derive the quadratic formula?
5. How do you find the vertex of a quadratic function using the completed square?

**Tip**: When completing the square, always remember to add the same value to both sides of the equation to maintain equality!

Brian is solving the equation x squared minus three-fourths x = 5. What value must be added to both sides of the equation to make the left side a perfect-square trinomial?

Learn how to complete the square for the quadratic equation x^2 - 3/4x = 5. This detailed step-by-step guide covers key algebraic concepts and explains how to transform the equation into a perfect-square trinomial by adding 9/64 to both sides. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation