1) x² -4[х]-21=0

To solve the equation x² - 4x - 21 = 0, you can use the quadratic formula. The quadratic formula states that for an equation of the form ax² + bx + c = 0, the solutions for x are given by: x = (-b ± √(b² - 4ac)) / (2a)

In this case, a = 1, b = -4, and c = -21. Substituting these values into the quadratic formula, we get:

x = (-(-4) ± √((-4)² - 4(1)(-21))) / (2(1)) x = (4 ± √(16 + 84)) / 2 x = (4 ± √(100)) / 2 x = (4 ± 10) / 2

Simplifying further, we get two possible solutions:

x₁ = (4 + 10) / 2 = 14 / 2 = 7 x₂ = (4 - 10) / 2 = -6 / 2 = -3

Therefore, the solutions to the equation x² - 4x - 21 = 0 are x = 7 and x = -3.