Question

Solve the equation for x, where x is a real number:
-2x^2 + 7x - 5 = 0

Answer 1

To find the solutions to this equation, we can apply the quadratic formula. This quadratic formula solves equations of the form ax^2 + bx + c = 0
x = [ -b ± √(b^2 - 4ac) ] / (2a)
x = [ -7 ± √((7)^2 - 4(-2)(-5)) ] / ( 2(-2) )
x = [-7 ± √(49 - (40) ) ] / ( -4 )
x = [-7 ± √(9) ] / ( -4)
x = [-7 ± 3 ] / ( -4 )
x = 7/4 ± -3/4
The answers are 7/4 + 3/4 = 5/2 and 1.

Answer 2

First you must know this.

`{ax}^(2) + bx + c = 0`
Then, you will know that a=-2 b=7 c=-5.
Now, use the quadratic formula.

`x = \frac{ \: - b + - \sqrt{ {b}^(2) - 4ac } }{2a}`

`x = \frac{ \: - 7 + - \sqrt{ {7}^(2) - 4( - 2)( - 5) } }{2 * - 2}`
You will then get two values for x.

`x = 1 \: and \: x = 2.5`
there you go! That's the answer.