Make x the subject of the formula: r = (1/2) * sqrt((b-x)/3)
Understand the Problem
The question asks to rearrange the given formula to make 'x' the subject. This involves isolating 'x' on one side of the equation by performing algebraic manipulations such as squaring, multiplication, and subtraction.
Answer
$x = b - 12r^2$
Answer for screen readers
$x = b - 12r^2$
Steps to Solve
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Multiply both sides by 2 To get rid of the fraction on the right side, we multiply both sides of the equation by 2: $2 * r = 2 * \frac{1}{2} \sqrt{\frac{b-x}{3}}$ $2r = \sqrt{\frac{b-x}{3}}$
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Square both sides To eliminate the square root, we square both sides of the equation: $(2r)^2 = (\sqrt{\frac{b-x}{3}})^2$ $4r^2 = \frac{b-x}{3}$
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Multiply both sides by 3 To get rid of the fraction on the right side, we multiply both sides of the equation by 3: $3 * 4r^2 = 3 * \frac{b-x}{3}$ $12r^2 = b - x$
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Isolate x To isolate $x$, we can add $x$ to both sides and subtract $12r^2$ from both sides: $12r^2 + x = b - x + x$ $12r^2 + x = b $ $12r^2 + x - 12r^2 = b - 12r^2$ $x = b - 12r^2$
$x = b - 12r^2$
More Information
The final answer expresses $x$ in terms of $b$ and $r$. This means that if we know the values of $b$ and $r$, we can easily calculate the value of $x$.
Tips
A common mistake is not squaring the entire term $2r$ in step 2. It is crucial to square both the 2 and the $r$, resulting in $4r^2$. Another common mistake is incorrectly applying the order of operations when isolating $x$, especially when dealing with negative signs.
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