How do you solve 2x²-x+8=0?

3 Answers
Jun 12, 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)(-1) for color(blue)(b)

color(green)(8) for color(green)(c) gives:

x = (-color(blue)(-1) +- sqrt(color(blue)(-1)^2 - (4 * color(red)(2) * color(green)(8))))/(2 * color(red)(2))

x = (1 +- sqrt(1 - 64))/4

x = (1 +- sqrt(-63))/4

x = (1 +- sqrt(63 * -1))/4

x = (1 +- sqrt(63)sqrt(-1))/4

The square root of -1 or sqrt(-1) is known as an imaginary number and is often referenced as i.

Substituting gives the solution set as;

x = {(1 - sqrt(63)i)/4, (1 +- sqrt(63)i)/4}

Jun 12, 2018

No real roots

Explanation:

y = 2x^2 - x + 8 = 0
Use the improved quadratic formula (Socratic, Google Search).
D = d^2 = b^2 - 4ac = 1 - 64 = -63
Since D < 0, there are no real roots.
There are 2 complex roots:
x = -b/(2a) +- d/(2a), with d = +- isqrt63
x = 1/4 +- (isqrt63)/4 = (1 +- isqrt63)/4

Jun 12, 2018

See below..

Explanation:

Let's complete the square:

2[x^2-1/2x]+8:

rArr 2(x-1/4)^2-1/16+128/16

rArr2(x-1/4)^2+127/16

rArr 2(x-1/4)^2=-127/16

rArr (x-1/4)^2=-127/32

x-1/4=pmsqrt(-127/32)

x=1/4pmsqrt(-127/32)

No real roots as negative square root, although you could use i, but I don't know how.