10x^2+13x-3=0

Question

solve and check the equation.

Answer 1

The equation is 10x^2 + 13x - 3 = 0.

Factor by grouping.

10x^2 + 15x - 2x - 3 = 0

5x(2x + 3) - 1(2x + 3) = 0

(2x + 3)(5x - 1) = 0

Factor : (2x + 3)(5x - 1) = 0

Apply zero product property.

(2x + 3) = 0 and (5x - 1) = 0

x = - 3/2, 1/5.

Solution of the equation is x = - 3/2, 1/5.

Check :

Substitute the value x = - 3/2 in 10x^2 + 13x - 3 = 0.

10(- 3/2)^2 + 13(- 3/2) - 3 = 0

(45/2) - (39/2) - 3 = 0

(45 - 39 - 6)/2 = 0

(45 - 45)/2 = 0

0/2 = 0

0 = 0.

The above statement is true, so x = - 3/2 is a solution of 10x^2 + 13x - 3 = 0.

Substitute the value x = 1/5 in 10x^2 + 13x - 3 = 0.

10(1/5)^2 + 13(1/5) - 3 = 0

(2/5) + (13/5) - 3 = 0

(2 + 13 - 15)/5 = 0

(15 - 15)/5 = 0

0/5 = 0

0 = 0.

The above statement is true, so x = 1/5 is a solution of 10x^2 + 13x - 3 = 0.