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Solve Quadratic Equation for -y^2+5y+36=0

Enter Quadratic equation/inequality below


   Hint Number =  
    
      
Solve the quadratic equation
-y2+5y+36 = 0

We have our a, b, and c values:
a = -1, b = 5, c = 36

Solve the quadratic equation
-y2 + 5y + 36=

Quadratic Formula

y  =  -b ± √b2 - 4ac
  2a

Calculate -b

-b = -(5)
-b = -5

Calculate the discriminant Δ

Δ = b2 - 4ac:
Δ = 52 - 4 x -1 x 36
Δ = 25 - -144
Δ = 169 <--- Discriminant
Since Δ > 0, we expect two real roots.

Take the square root of Δ

√Δ = √(169)
√Δ = 13

-b + Δ:

Numerator 1 = -b + √Δ
Numerator 1 = -5 + 13
Numerator 1 = 8

-b - Δ:

Numerator 2 = -b - √Δ
Numerator 2 = -5 - 13
Numerator 2 = -18

Calculate 2a

Denominator = 2 * a
Denominator = 2 * -1
Denominator = -2

Find Solutions

Solution 1  =  Numerator 1
  Denominator

Solution 1  =  8
  -2

  Solution 1  =  -4

Solution 2  =  Numerator 2
  Denominator

Solution 2  =  -18
  -2

  Solution 2  =  9

Solution Set

(Solution 1, Solution 2) = (-4, 9)

Prove our first answer

(-4)2 + 5(-4) + 36 ? 0
(16) - 2036 ? 0
-16 - 2036 ? 0
0 = 0

Prove our second answer

(9)2 + 5(9) + 36 ? 0
(81) + 4536 ? 0
-81 + 4536 ? 0
0 = 0






What is the Answer?

(Solution 1, Solution 2) = (-4, 9)

How does the Quadratic Equations and Inequalities Calculator work?

Free Quadratic Equations and Inequalities Calculator - Solves for quadratic equations in the form ax2 + bx + c = 0. Also generates practice problems as well as hints for each problem.
* Solve using the quadratic formula and the discriminant Δ
* Complete the Square for the Quadratic
* Factor the Quadratic
* Y-Intercept
* Vertex (h,k) of the parabola formed by the quadratic where h is the Axis of Symmetry as well as the vertex form of the equation a(h - h)2 + k
* Concavity of the parabola formed by the quadratic
* Using the Rational Root Theorem (Rational Zero Theorem), the calculator will determine potential roots which can then be tested against the synthetic calculator.
This calculator has 4 inputs.

What 5 formulas are used for the Quadratic Equations and Inequalities Calculator?

  1. y = ax2 + bx + c
  2. (-b ± √b2 - 4ac)/2a
  3. h (Axis of Symmetry) = -b/2a
  4. The vertex of a parabola is (h,k) where y = a(x - h)2 + k

For more math formulas, check out our Formula Dossier

What 9 concepts are covered in the Quadratic Equations and Inequalities Calculator?

complete the square
a technique for converting a quadratic polynomial of the form ax2 + bx + c to a(x - h)2 + k
equation
a statement declaring two mathematical expressions are equal
factor
a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n.
intercept
parabola
a plane curve which is approximately U-shaped
quadratic
Polynomials with a maximum term degree as the second degree
quadratic equations and inequalities
rational root
vertex
Highest point or where 2 curves meet

Example calculations for the Quadratic Equations and Inequalities Calculator

  1. 4x^2+11x-3
  2. a^2-a+6
  3. x^2 + 7x + 6>=0
  4. x^2+2x=35

Quadratic Equations and Inequalities Calculator Video


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