Question - Solving a Quadratic Equation
mathsolving quadratic equationquadratic equation solutionsimplify square root termssolving equations with fractions
Solution:
The equation in the image is:\[ 2r + 2 \sqrt{r^2} + \frac{r}{2} = 10 \]To solve this equation for $$ r $$, follow these steps:1. Simplify the square root term. Since $$ \sqrt{r^2} $$ is the square root of a square, it simplifies to $$ r $$ if $$ r \geq 0 $$ (assuming $$ r $$ is non-negative, as you cannot take the square root of a negative number in real numbers).So, you have:\[ 2r + 2r + \frac{r}{2} = 10 \]\[ 4r + \frac{r}{2} = 10 \]2. Combine like terms by finding a common denominator for the $$ r $$-terms.Multiply each term by 2 to get rid of the fraction:\[ 2 \cdot 4r + 2 \cdot \frac{r}{2} = 2 \cdot 10 \]\[ 8r + r = 20 \]\[ 9r = 20 \]3. Divide both sides by 9 to solve for $$ r $$:\[ r = \frac{20}{9} \]Therefore, $$ r = \frac{20}{9} $$ or approximately 2.2222.
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