Answer:
x = -3
x = 1/2
Step-by-step explanation:
[tex]2x^2+5x-3=0[/tex]
quadratic equation format: [tex]ax^2+bx+c=0[/tex]
Find the factors of the product of [tex]a[/tex] and [tex]c[/tex] that sum to [tex]b[/tex]
product of a and c: 2 x -3 = -6
Factors of -6 that sum to 5: 6 and -1
Therefore, rewrite the equation as 2x² + 6x - x - 3 = 0
Break the equation into groups:
⇒ (2x² + 6x) - (x + 3) = 0
Factor the brackets:
⇒ 2x(x + 3) - 1(x + 3) = 0
Factor out common factor (x + 3):
⇒ (2x - 1)(x + 3) = 0
Therefore, 2x - 1 = 0 ⇒ x = 1/2
And, x + 3 = 0 ⇒ x = -3
