Answer:
the solutions to the equation x^2 + 5x = 3 are:
x = (-5 + √37) / 2
x = (-5 - √37) / 2
Explanation:
Step 1: Move the constant term to the other side of the equation, so we have 0 on one side:
x^2 + 5x - 3 = 0
Step 2: Now, we can attempt to factorize the quadratic equation. However, in this case, it is not easily factorizable. So, we will use the quadratic formula to find the solutions.
The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a), where the equation is in the form ax^2 + bx + c = 0.
In our equation x^2 + 5x - 3 = 0, a = 1, b = 5, and c = -3.
Step 3: Substitute the values of a, b, and c into the quadratic formula:
x = (-5 ± √(5^2 - 4(1)(-3))) / (2*1)
Step 4: Simplify the equation:
x = (-5 ± √(25 + 12)) / 2
x = (-5 ± √37) / 2
Therefore, the solutions to the equation x^2 + 5x = 3 are:
x = (-5 + √37) / 2
x = (-5 - √37) / 2