Question

Solve the quadratic equation by factoring. 2x^2+9x-5=0This factors into (x+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

x = -5 and x = 0.5

Step-by-step explanation:

The factors of 2x² + 9x - 5 = 0 should have 5 and 1 as constants because these numbers are the only factors of 5. Therefore, the factors are:

( x + 5)(2x - 1)

because:

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

(x + 5)(2x - 1) = 2x² - x + 10x - 5

(x + 5)(2x - 1) = 2x² + 9x - 5

Then,(x + 5)(2x - 1) = 0 is equal to 0 if one of the factors are equal to zero. So, the solutions are:

x + 5 = 0

x + 5 - 5 = 0 - 5

x = -5

2x - 1 = 0

2x - 1 + 1 = 0 + 1

2x = 1

2x/2 = 1/2

x = 1/2 = 0.5

So, the answers are:

x = -5 and x = 0.5