l Solve Quadratic Equation for -x^2+12x+540=575

Enter Quadratic equation/inequality below

Hint Number =

Solve the quadratic:

-x2+12x+540 = 575

The quadratic you entered is not in standard form:
ax2 + bx + c = 0

Subtract 575 from both sides

-x2+12x+540 - 575 = 575 - 575

Simplifying, we get:

-x2+12x-35 = 0

Set up the a, b, and c values:

a = -1, b = 12, c = -35

Quadratic Formula

x  =  -b ± √b2 - 4ac
  2a

Calculate -b

-b = -(12)

-b = -12

Calculate the discriminant Δ

Δ = b2 - 4ac:

Δ = 122 - 4 x -1 x -35

Δ = 144 - 140

Δ = 4 <--- Discriminant

Since Δ > 0, we expect two real roots.

Take the square root of Δ

Δ = √(4)

Δ = 2

-b + Δ:

Numerator 1 = -b + √Δ

Numerator 1 = -12 + 2

Numerator 1 = -10

-b - Δ:

Numerator 2 = -b - √Δ

Numerator 2 = -12 - 2

Numerator 2 = -14

Calculate 2a

Denominator = 2 * a

Denominator = 2 * -1

Denominator = -2

Find Solutions

Solution 1  =  Numerator 1
  Denominator

Solution 1  =  -10
  -2

Solution 1 = 5

Solution 2

Solution 2  =  Numerator 2
  Denominator

Solution 2  =  -14
  -2

Solution 2 = 7

Solution Set

(Solution 1, Solution 2) = (5, 7)


Prove our first answer

(5)2 + 12(5) - 35 ? 0

(25) + 6035 ? 0

-25 + 6035 ? 0

0 = 0

Prove our second answer

(7)2 + 12(7) - 35 ? 0

(49) + 8435 ? 0

-49 + 8435 ? 0

0 = 0

Final Answer


(Solution 1, Solution 2) = (5, 7)