Algebra

x^2 + 3 = 4

Step-by-step solution with explanation

Final Answer

and

Step-by-step solution

1

Write the equation to solve

We start by writing the equation clearly so we know exactly what we need to solve.
2

Subtract 3 from both sides

We want to isolate the term. Subtracting 3 from both sides keeps the equation balanced.
3

Simplify both sides

The left side simplifies to and the right side simplifies to .
4

Take the square root of both sides

To solve for , we take the square root of both sides. We must include both the positive and negative square root, since both can be squared to give .
5

State both solutions

Since , our two solutions are and . Both check out: and .

Understanding this problem

Learning Insight

Whenever you solve , there are always TWO solutions if : one positive and one negative. This is because squaring always makes a number positive, so both and squared equal . This is called the 'plus-or-minus' principle.

Quick Tip

After isolating , just ask yourself: 'What number times itself equals the right side?' Then write BOTH the positive and negative versions of that number.

Common Mistake

Students often forget the negative solution and only write . Any time you take a square root while solving an equation, you MUST write to capture both answers.