How do you solve 10x^2-31x+15=0 using the quadratic formula?

2 Answers
smendyka
Jun 12, 2017

See a solution process below:

Explanation:

From: http://www.purplemath.com/modules/quadform.htm

The quadratic formula states:

For ax^2 + bx + c = 0, the values of x which are the solutions to the equation are given by:

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

Substituting 10 for a; -31 for b and 15 for c gives:

x = (-(-31) +- sqrt((-31)^2 - (4 * 10 * 15)))/(2 * 10)

x = (31 +- sqrt(961 - 600))/20

x = (31 +- sqrt(361))/20

x = (31 +- 19)/20

x = 50/20 and x = 12/20

x = 5/2 and x = 3/5

Nghi N
Jun 12, 2017

5/2, 6/5

Explanation:

Use the improved quadratic formula (Google, Socratic Search).
f(x) = 10x^2 - 31x + 15 = 0
D = d^2 = b^2 - 4ac = 961 - 600 = 361 --> d = +- 19
There are 2 real roots:
x = -b/(2a) +- d/(2a) = 31/20 +- 19/20 = (31 +- 19)/20
x1 = 50/20 = 5/2
x2 = 12/20 = 3/5

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