Solve for x: $5x^2 = 20$
Understand the Problem
The question asks to solve the equation $5x^2 = 20$ by finding the value of $x$ that satisfies the equation. First divide both sides by 5, then take the square root of both sides of the equation.
Answer
$x = \pm 2$
Answer for screen readers
$x = 2$ or $x = -2$
Steps to Solve
- Divide both sides by 5
To isolate the $x^2$ term, divide both sides of the equation by 5: $$ \frac{5x^2}{5} = \frac{20}{5} $$ $$ x^2 = 4 $$
- Take the square root of both sides
Take the square root of both sides of the equation to solve for $x$. Remember that when taking the square root, there are both positive and negative solutions. $$ \sqrt{x^2} = \pm \sqrt{4} $$ $$ x = \pm 2 $$
$x = 2$ or $x = -2$
More Information
The solutions to the equation are $x = 2$ and $x = -2$. Both of these values, when squared and multiplied by 5, will result in 20. Numbers have both a positive and a negative square root.
Tips
A common mistake is forgetting to consider both the positive and negative square roots when solving for $x$. Always remember that when you take the square root of a number, both the positive and negative values are possible solutions.
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