l Solve Quadratic Equation for x^2+x-12=0

Enter Quadratic equation/inequality below

Hint Number =

Solve the quadratic:

x2+x-12 = 0

Set up the a, b, and c values:

a = 1, b = 1, c = -12

Quadratic Formula

x  =  -b ± √b2 - 4ac
  2a

Calculate -b

-b = -(1)

-b = -1

Calculate the discriminant Δ

Δ = b2 - 4ac:

Δ = 12 - 4 x 1 x -12

Δ = 1 - -48

Δ = 49 <--- Discriminant

Since Δ > 0, we expect two real roots.

Take the square root of Δ

Δ = √(49)

Δ = 7

-b + Δ:

Numerator 1 = -b + √Δ

Numerator 1 = -1 + 7

Numerator 1 = 6

-b - Δ:

Numerator 2 = -b - √Δ

Numerator 2 = -1 - 7

Numerator 2 = -8

Calculate 2a

Denominator = 2 * a

Denominator = 2 * 1

Denominator = 2

Find Solutions

Solution 1  =  Numerator 1
  Denominator

Solution 1  =  6
  2

Solution 1 = 3

Solution 2

Solution 2  =  Numerator 2
  Denominator

Solution 2  =  -8
  2

Solution 2 = -4

Solution Set

(Solution 1, Solution 2) = (3, -4)


Prove our first answer

(3)2 + 1(3) - 12 ? 0

(9) + 312 ? 0

9 + 312 ? 0

0 = 0

Prove our second answer

(-4)2 + 1(-4) - 12 ? 0

(16) - 412 ? 0

16 - 412 ? 0

0 = 0

Final Answer


(Solution 1, Solution 2) = (3, -4)