Question

Solve the quadratic equation.

6^{2} = 5x + 6

I would appreciate help with this, thanks in advance!

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Answer 1

Explanation:

are you sure this is the whole information ?

because

6² = 5x + 6

is not called a quadratic equation.

it is a quadratic equation, when there is one term in x² involved.

I assume therefore, that your problem is

6x² = 5x + 6

that is then as basic quadratic equation

6x² - 5x - 6 = 0

the general solution to a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

a = 6

b = -5

c = -6

x = (5 ± sqrt((-5)² - 4×6×-6))/(2×6) =

= (5 ± sqrt(25 + 144))/12 = (5 ± sqrt(169))/12 =

= (5 ± 13)/12

x1 = (5 + 13)/12 = 18/12 = 3/2

x2 = (5 - 13)/12 = -8/12 = -2/3

so, the 2 solutions for the quadratic equation are

x = 3/2 and x = -2/3

Answer 2

`6 {x}^(2) - 5x - 6 = 0 \\ 6 {x}^(2) - 9x + 4x - 6 = 0 \\ (6 {x}^(2) - 9x) + (4x - 6) = 0 \\ 3x(2x - 3) + 2(2x - 3) = 0 \\ (3x + 2)(2x - 3) = 0 \\ 3x + 2 = 0 \\ \\ \\ or \\ 2x - 3 = 0 \\ x = ( - 2)/(3) \\ \\ or \\ \\ x = (3)/(2)`

I FACTORISED THE EQUATION FIRST WITH A SIMPLE METHOD OF MULTIPLYING THE COEFFICIENT OF

`{x}^(2)`

and the constant number then find the factors that will give me the coefficient of x.

ATTACHED IS THE SOLUTION