To solve the equation 2x² + 3x – 7 + x² + 5x – 39 = 0, we first need to combine like terms.
Start by combining the x² terms:
- 2x² + x² = 3x²
Next, combine the x terms:
- 3x + 5x = 8x
Now, combine the constant terms:
- -7 – 39 = -46
Putting it all together, our equation simplifies to:
3x² + 8x – 46 = 0
Next, we can use the quadratic formula to find the solutions for x, which is given by:
x = (-b ± √(b² – 4ac)) / 2a
In our equation, the coefficients are:
- a = 3
- b = 8
- c = -46
Now plug these values into the quadratic formula:
- b² – 4ac = 8² – 4 * 3 * (-46) = 64 + 552 = 616
Now we can calculate x:
- x = (−8 ± √616) / (2 * 3)
- x = (−8 ± 24.8) / 6
This gives us two potential solutions:
- x = (16.8) / 6 = 2.8
- x = (−32.8) / 6 = -5.467
Thus, the two solutions for the equation are:
- x = 2.8
- x ≈ -5.467