Final answer:
To solve the quadratic equation x^2 - 4x - 9 = 29, it is first simplified to x^2 - 4x - 38 = 0. Using the quadratic formula, we find the solutions x = 4 + √(42) and x = 4 - √(42).
Step-by-step explanation:
To solve the quadratic equation x^2 - 4x - 9 = 29, we first need to bring the equation to the standard quadratic form ax^2 + bx + c = 0. By subtracting 29 from both sides, we get x^2 - 4x - 38 = 0.
Next, we use the quadratic formula x = -b ± √(b^2 - 4ac) / 2a to find the values of x. Substituting the coefficients from our equation (a = 1, b = -4, c = -38) into the formula gives us:
x = -(-4) ± √((-4)^2 - 4*1*(-38)) / (2*1)
x = 4 ± √(16 + 152) / 2
x = 4 ± √(168) / 2
x = 4 ± √(4*42) / 2
x = 4 ± 2√(42) / 2
x = 4 ± √(42)
The solutions are x = 4 + √(42) and x = 4 - √(42).