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Solve quadratic equation using the formula method

Question

Solve the quadratic equation 6x2 - x - 1 = 0 using the formula method

Solution

The standard form of the quadratic equation is ax2 + bx + c = 0. Compare the given equation with the standard equation, we get, a = 6, b = -1 and c = -1.

The formula to solve quadratic equation is x1,2 = [-b + - square root of b2 - 4ac]/2a

substitude a, b and c into the formula
x1,2 = [-b + - square root of b2 - 4ac]/2a
= [-(-1) + - square root of (-1)2 - 4(6)(-1)]/2(6)
= [1 + - square root of 1 + 24]/12
= [1 + - square root of 25/12
= [1 + - 5]/12
so, we get two equations, one is x = (1 + 5)/12 and other is (1 - 5)/12
if x = (1 + 5)/12, then x = 6/12 = 1/2
if x = (1 - 5)/12, then x = -4/12 = -1/3
so, we get two solutions, x1 = 1/2 and x2 = -1/3

Substitute x1 = 1/2 and x2 = -1/3 into the original equation, find that the left side of the equation is equal to the right side of the equation. So, x1 = 1/2 and x2 = -1/3 are the solutions of original equation.