let _ be any of these numbers: -20, -8, -2, 3,4, 5, 14, 15, 21. Just because 1 _ in the equation = -2, it does NOT mean all _s= -2. the equation is: (_x+_)+(_x+_)=_x^2+_x+_. which numbers should go in the _s to make the equation true? Put them in the left to right order

We are given an equation of the form:

\[
(_x + _) + (_x + _) = _x^2 + _x + _
\]

And we need to fill in the blanks with numbers from the set \{-20, -8, -2, 3, 4, 5, 14, 15, 21\}, ensuring that the equation holds true.

### Step 1: Expand the left-hand side

The left-hand side is:

\[
(_x + _) + (_x + _) = 2_x + 2_
\]

This simplifies to:

\[
2_x + 2_ = 2x + 2
\]

### Step 2: Examine the right-hand side

The right-hand side is:

\[
_x^2 + _x + _
\]

Which becomes:

\[
x^2 + x + _
\]

### Step 3: Compare both sides of the equation

We need to match the terms on both sides. This gives us two key observations:

1. The degree of \(x^2\) term should match on both sides.
2. The coefficients of \(x\) and the constant terms should match as well.

### Step 4: Solve for the coefficients

The right-hand side has a quadratic term \(x^2\). Therefore, on the left-hand side, there must be no \(x^2\) term, which leads us to conclude that one of the blank spaces on the right must be set to ensure both sides balance.



Let _ be any of these numbers: -20, -8, -2, 3, 4, 5, 14, 15, 21. Just because 1 _ in the equation = -2, it does NOT mean all _s= -2. The equation is: (_x+_)+(_x+_)=_x^2+_x+_. Which numbers should go in the _s to make the equation true? Put them in the left to right order.

Discover how to solve a quadratic equation by filling in blanks with values from a given set: {-20, -8, -2, 3, 4, 5, 14, 15, 21}. This step-by-step guide explains key algebraic concepts and equation balancing, ideal for students in Grades 8-10.

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