Solve the equation x^2 + 4 = 8
Understand the Problem
The question is asking to solve the quadratic equation x^2 + 4 = 8 for the variable x. It involves algebraic manipulation to isolate x and find its value(s).
Answer
$x = \pm 2$
Answer for screen readers
$x = 2$ and $x = -2$
Steps to Solve
- Isolate the $x^2$ term
Subtract 4 from both sides of the equation to isolate the $x^2$ term:
$$x^2 + 4 - 4 = 8 - 4$$
$$x^2 = 4$$
- Solve for $x$ by taking the square root
Take the square root of both sides of the equation:
$$\sqrt{x^2} = \sqrt{4}$$
Remember to consider both positive and negative roots:
$$x = \pm 2$$
- Final Answer
Therefore, the solutions for $x$ are $x = 2$ and $x = -2$.
$x = 2$ and $x = -2$
More Information
The solutions to the quadratic equation $x^2 + 4 = 8$ are $2$ and $-2$. These are the values of $x$ that, when squared and added to 4, equal 8.
Tips
A common mistake is forgetting to include both the positive and negative square roots when solving for $x$. Only taking the positive root would give only one of the two correct answers. To avoid this, always remember that a number has two square roots: a positive and a negative one.
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