The Product Of -7 And A Number Squared Is -28

Introduction

The product of -7 and a number squared is -28, a concise algebraic statement that invites us to determine the unknown value through systematic reasoning. In this article we will explore how to translate this verbal description into a mathematical equation, solve it step by step, and understand the underlying concepts that make such problems solvable. By the end of the guide, readers will not only find the numerical answer but also gain confidence in handling similar expressions involving negative coefficients and squared terms. This approach combines clear instruction with practical examples, ensuring that learners from diverse backgrounds can follow along and apply the method to real‑world scenarios.

Steps

Setting up the equation

1. Identify the unknown – Let the unknown number be represented by x.
2. Translate the words into symbols – “the product of -7 and a number squared” becomes (-7 \times x^{2}).
3. Set the expression equal to the given value – The statement says the product “is -28”, so we write (-7x^{2} = -28).

Solving for the variable

1. Isolate the squared term – Divide both sides of the equation by -7:

   [ \frac{-7x^{2}}{-7} = \frac{-28}{-7} ]

   This simplifies to (x^{2} = 4).

2. Take the square root of both sides – Remember that the square root of a positive number yields both a positive and a negative solution:

   [ x = \pm\sqrt{4} ]

   Hence, (x = \pm 2) Still holds up..

3. Write the final answer – The two possible values for the number are 2 and -2 And it works..

Verifying the solution

• For (x = 2): (-7 \times (2)^{2} = -7 \times 4 = -28) ✔️
• For (x = -2): (-7 \times (-2)^{2} = -7 \times 4 = -28) ✔️

Both values satisfy the original statement, confirming that the product of -7 and a number squared is -28 when the number is either 2 or -2.

Common pitfalls and how to avoid them

• Forgetting the negative sign when dividing by -7; always keep track of sign changes.
• Ignoring the ± symbol when taking square roots; both positive and negative roots must be considered.
• Misreading “squared” as “square root”; the phrase “a number squared” means the number is multiplied by itself, not the opposite operation.

Scientific Explanation

The equation (-7x^{2} = -28) is a quadratic equation because it contains the variable raised to the second power. Quadratic equations generally take the form (ax^{2} + bx + c = 0). In our case, the coefficient a equals -7, b equals 0 (there is no linear term), and c equals 28 after