Answer:
x = - 3 , x = [tex]\frac{1}{5}[/tex]
Step-by-step explanation:
given the quadratic equation
15x² + 42x= 9 ( subtract 9 from both sides )
15x² + 42x - 9 = 0 ← in standard form
To factorise
Consider the factors of the product of the coefficient of the x²- term and the constant term which sum to give the coefficient of the x- term.
product = 15 × - 9 = - 135 and sum = + 42
The factors are + 45 and - 3
Use these factors to split the x- term
15x² + 45x - 3x - 9 = 0 ( factor the first/second and third/fourth terms )
15x(x + 3) - 3(x + 3) = 0 ← factor out (x + 3) from each term
(x + 3)(15x - 3) = 0 ← in factored form
equate each factor to zero and solve for x
x + 3 = 0 ⇒ x = - 3
15x - 3 = 0 ⇒ 15x = 3 ⇒ x = [tex]\frac{3}{15}[/tex] = [tex]\frac{1}{5}[/tex]
The solutions are x = - 3 , x = [tex]\frac{1}{5}[/tex]
