Solve 2x^2 + 19x - 145 = 0?

3 Answers
Mar 15, 2018

See a solution process below:

Explanation:

We can use the quadratic equation to solve this problem:

The quadratic formula states:

For color(red)(a)x^2 + color(blue)(b)x + color(green)(c) = 0, the values of x which are the solutions to the equation are given by:

x = (-color(blue)(b) +- sqrt(color(blue)(b)^2 - (4color(red)(a)color(green)(c))))/(2 * color(red)(a))

Substituting:

color(red)(2) for color(red)(a)

color(blue)(19) for color(blue)(b)

color(green)(-145) for color(green)(c) gives:

x = (-color(blue)(19) +- sqrt(color(blue)(19)^2 - (4 * color(red)(2) * color(green)(-145))))/(2 * color(red)(2))

x = (-19 +- sqrt(361 - (8 * color(green)(-145))))/4

x = (-19 +- sqrt(361 - (-1160)))/4

x = (-19 +- sqrt(361 + 1160))/4

x = (-19 +- sqrt(1521))/4

x = (-19 - 39)/4 and x = (-19 + 39)/4

x = (-58)/4 and x = 20/4

x = -14.5 and x = 5

The Solution Set Is: x = {-14.5, 5}

Mar 15, 2018

See details below....

Explanation:

2x^2+19x-145=0

Start by factoring the the left side

(2x + 29)(x-5)

Then set factors equal to 0

2x + 29 = 0 or x-5=0

2x = 0 - 29 or x= 0 + 5

2x = -29 or x=5

x = (-29)/2 or x=5

Mar 15, 2018

By using the quadratic formula, we find that x=5 and x=-14.5

Explanation:

The quadratic formula takes an equation that looks like this:

ax^2+bx+c

And plugs it into a formula that solves for x:

(-b+-sqrt(b^2-4ac))/(2a)

Based on our equation, we know the values of a, b, and c:

a=2
b=19
c=-145

(-19+-sqrt(19^2-4(2xx-145)))/(2(2))

(-19+-sqrt(361+1160))/4 rArr (-19+-sqrt(1521))/4

(-19+-39)/4 rArr x=[5, -14.5]