Question

Solve the quadratic equation by factoring. 6x^2+17x+5=0This factors into (3x+Answer)(2x+Answer=0)Enter your solutions below from smallest to largest. If a solution is repeated type that answer for both values of x. If your answer is not an integer then type it as a decimal rounded to the nearest hundredth.x=Answer and x=Answer

Answer 1

given,

6x^2 + 17x + 5 = 0

to solvre this, factor left hand side by grouping.

Firstly, left hand side needs to be rewritten as

6x^2 + ax + bx + 5

lets set up a system to find a and b

a + b = 17

ab = 6 x 5 = 30

after bearing this in mind,

lets rewrite 6x^2 + 17x + 5 as

(6x^2 + 2x) + (15x + 5)

lets factor out 2x in the first and 5 in the second group

so,

2x(3x + 1) + 5(3x + 1)

lets factor out common terms 3x + 1

(3x + 1) (2x + 5)

to find the equation solutions,

3x + 1 = 0 and 2x + 5 = 0

so,

3x = -1 and 2x = -5

x = -1/3 and x = -5/2

x = -0.3 and x = -2.5

so x = -0.3, -2.5 (in decimal form)