To solve the quadratic equation x² + 2x – 22 = 0, we can use the quadratic formula, which is:
x = (-b ± √(b² – 4ac)) / 2a
In this equation, a, b, and c represent the coefficients from the standard form of a quadratic equation ax² + bx + c = 0. Here, a = 1, b = 2, and c = -22.
First, we need to calculate the discriminant (b² – 4ac):
b² – 4ac = 2² – 4(1)(-22) = 4 + 88 = 92
Since the discriminant is positive, there will be two distinct real solutions. Now, let’s substitute the values into the quadratic formula:
x = (-2 ± √92) / 2(1)
We can simplify √92:
√92 = √(4 × 23) = 2√23
Now substituting this back into the formula:
x = (-2 ± 2√23) / 2
We can simplify this further:
x = -1 ± √23
Thus, the two solutions for the quadratic equation x² + 2x – 22 = 0 are:
x = -1 + √23 and x = -1 – √23