To solve the quadratic equation x² + 4x – 18 = 0, we can use the quadratic formula, which is given by:
x = (-b ± √(b² – 4ac)) / 2a
In our equation, we can identify the coefficients as follows:
- a = 1 (the coefficient of x²)
- b = 4 (the coefficient of x)
- c = -18 (the constant term)
Next, we substitute these values into the quadratic formula:
x = (-(4) ± √((4)² – 4(1)(-18))) / 2(1)
This simplifies to:
x = (-4 ± √(16 + 72)) / 2
Now, let’s simplify under the square root:
x = (-4 ± √(88)) / 2
Since √(88) can be simplified further (because 88 = 4 × 22), we have:
√(88) = 2√(22)
Now we substitute this back into our equation:
x = (-4 ± 2√(22)) / 2
This can be simplified further by dividing both terms in the numerator by 2:
x = -2 ± √(22)
Thus, the solutions to the equation x² + 4x – 18 = 0 are:
- x = -2 + √(22)
- x = -2 – √(22)
In decimal form, these values can be approximated if needed:
- x ≈ 0.69
- x ≈ -4.69
This gives us the complete and detailed solution to the quadratic equation!