To find the two solutions of the equation x² + 2x – 4 = 3x + 9, we first need to rearrange it into a standard quadratic form.
Start by moving all terms to one side:
x² + 2x – 4 – 3x – 9 = 0
Combine like terms:
x² – x – 13 = 0
Next, we can use the quadratic formula to solve for x. The quadratic formula is:
x = (-b ± √(b² – 4ac)) / (2a)
In our equation, a = 1, b = -1, and c = -13. Substituting these values into the formula gives:
x = (1 ± √((-1)² – 4(1)(-13))) / (2(1))
x = (1 ± √(1 + 52)) / 2
x = (1 ± √53) / 2
This results in two solutions:
x = (1 + √53) / 2
x = (1 – √53) / 2
Thus, the two solutions to the equation are:
- x = (1 + √53) / 2
- x = (1 – √53) / 2