Question

Equations and Inequalities: Mastery Test Enter the correct answer in the box. Replace the values of m and n to show the solutions of this equation. x²+6x-5=0

Answer 1

To solve the quadratic equation x² + 6x - 5 = 0, the quadratic formula is used. The solutions are x = -3 + sqrt(7) and x = -3 - sqrt(7).

Step-by-step explanation:

The given equation is x² + 6x - 5 = 0, which is a quadratic equation of the form ax² + bx + c = 0. To find the solutions for x, we can use the quadratic formula, which is x = [-b ± sqrt(b² - 4ac)] / (2a). In this case, a = 1, b = 6, and c = -5. Substituting these into the quadratic formula gives us:

x = [-6 ± sqrt(6² - 4(1)(-5))] / (2(1))

x = [-6 ± sqrt(36 + 20)] / 2

x = [-6 ± sqrt(56)] / 2

x = [-6 ± sqrt(4²7)] / 2

x = [-6 ± 2sqrt(7)] / 2

x = -3 ± sqrt(7)

Therefore, the solutions for the equation x² + 6x - 5 = 0 are x = -3 + sqrt(7) and x = -3 - sqrt(7).