Question

Solving equations using quadratic formula m² -5m - 14 = 0

Answer 1

x = 7 ; -2

Step-by-step explanation:

Solving equations using quadratic formula:

`\sf \boxed{\bf x = (-b \± √(b^2 - 4ac))/(2a)}`

m² - 5m - 14 = 0

a = 1 ; b = -5 ; c = -14

b² - 4ac = (-5)² - 4 *(1)*(-14)

= 25 + 56

= 81

`\sf x = (-(-5) \± √(81))/(2*1)\\\\x = (5 \± 9)/(2)\\\\\\x = (5+9)/(2) \ ; x =(5-9)/(2)\\\\\\x = (14)/(2) \ ; x =(-4)/(2)\\\\`

x = 7 or -2

Answer 2

Given:

an equation is given as m² -5m - 14 = 0

Find:

we have to solve the given quadratic equation.

Step-by-step explanation:

Compare the given equation with am² + bm + c = 0, we get

a = 1, b = -5, c = -14

we will solve the given equation as following

`\begin{gathered} ()=(-b\pm√(b^2-4ac))/(2a)=(-(-5)\pm√((-5)^2-4(1)(-14)))/(2(1)) \\ ()=(5\pm√(25+56))/(2)=(5\pm√(81))/(2) \\ ()=(5\pm9)/(2) \\ ()=(5+9)/(2),(5-9)/(2) \\ ()=(14)/(2),-(4)/(2) \\ ()=7,-2 \end{gathered}`

Therefore, the solution of given equation is m = 7, -2