i am stuck with this problem:
Problem #12
Solve by using the quadratic formula.
5x^2 + 5x = 3
i am at this step
x = (-5 (+/-) sqrt (85))/(10)
you are done!
Great job! You are almost there. You have correctly applied the quadratic formula to solve the equation 5x^2 + 5x = 3. The next step is to simplify the expression:
x = (-5 ± √(85))/(10)
You have correctly written the solutions in the "plus-minus" form, which means there is one solution with a positive sign and another solution with a negative sign.
Now, if you would like to find the actual numeric solutions, you can simplify further by evaluating the square root of 85 and then performing the division.
Let's break it down step by step:
1. Start with x = (-5 ± √(85))/(10).
2. Simplify the square root of 85. It cannot be simplified any further because it is not a perfect square. So, √(85) remains as it is.
3. Divide each term in the numerator by 10. This gives us:
x = -0.5 ± (√(85))/(10)
Therefore, the final solutions for x are:
x = (-0.5 + √(85))/(10)
and
x = (-0.5 - √(85))/(10)
Keep up the good work!