Solve Using Quadratic Equation
5r^2 = 2r + 1
5r^2 = 2r + 1
5r^2 - 2r - 1 = 0
Now use the Quadratic Equation Formula.
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To solve the quadratic equation 5r^2 = 2r + 1, we need to rearrange it into the standard quadratic equation form: ax^2 + bx + c = 0. In this case, we have:
5r^2 - 2r - 1 = 0
Now, we can use the quadratic formula, which states that for any quadratic equation in the form ax^2 + bx + c = 0, the solutions can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Applying this formula to our equation, we have:
r = (-(-2) ± √((-2)^2 - 4(5)(-1))) / (2(5))
r = (2 ± √(4 + 20)) / 10
r = (2 ± √24) / 10
r = (2 ± 2√6) / 10
Simplifying further:
r = (1 ± √6) / 5
Thus, the solutions to the quadratic equation 5r^2 = 2r + 1 are r = (1 + √6) / 5 and r = (1 - √6) / 5.