Question

Solve the following quadratic equation
5х2 - 10x – 21 = 39​

Answer 1

x=1+√13 or x=1−√13

Explanation:

Step 1: Subtract 39 from both sides.

5x2−10x−21−39=39−39

5x2−10x−60=0

For this equation: a=5, b=-10, c=-60

5x2+−10x+−60=0

Step 2: Use quadratic formula with a=5, b=-10, c=-60.

x=

−b±√b2−4ac

2a

x=

−(−10)±√(−10)2−4(5)(−60)

2(5)

x=

10±√1300

10

x=1+√13 or x=1−√13

Answer 2

Explanation:

Rewrite this quadratic in standard form by subtracting 39 from both sides. We get:

5x^2 - 10x - 60 = 0

Reduce this by dividing all four terms by 5:

x^2 - 2x - 12 = 0

Use the quadratic equation to find the roots. The coefficients of the x terms are 1, -2, -12. Thus the discriminant is b^2 - 4ac, or:

(-2)^2 - 4(1)(-12) = -44 of which 4 is a perfect square factor and 11 is not.

Because the discriminant is negative, the given equation has two unequal, complex roots, which are:

-(-10) ± i√4√11

x = -----------------------

10

or x = 1 ± (1/5)√11