0=(1.39*h^2)-(1141.6*h)-1222849

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Solution for 0=(1.39*h^2)-(1141.6*h)-1222849 equation:


Simplifying
0 = (1.39h2) + -1(1141.6h) + -1222849

Remove parenthesis around (1141.6h)
0 = (1.39h2) + -1 * 1141.6h + -1222849

Multiply -1 * 1141.6
0 = (1.39h2) + -1141.6h + -1222849

Reorder the terms:
0 = -1222849 + -1141.6h + (1.39h2)

Solving
0 = -1222849 + -1141.6h + (1.39h2)

Solving for variable 'h'.

Combine like terms: 0 + 1222849 = 1222849
1222849 + 1141.6h + (-1.39h2) = -1222849 + -1141.6h + (1.39h2) + 1222849 + 1141.6h + (-1.39h2)

Reorder the terms:
1222849 + 1141.6h + (-1.39h2) = -1222849 + 1222849 + -1141.6h + 1141.6h + (1.39h2) + (-1.39h2)

Combine like terms: -1222849 + 1222849 = 0
1222849 + 1141.6h + (-1.39h2) = 0 + -1141.6h + 1141.6h + (1.39h2) + (-1.39h2)
1222849 + 1141.6h + (-1.39h2) = -1141.6h + 1141.6h + (1.39h2) + (-1.39h2)

Combine like terms: -1141.6h + 1141.6h = 0.0
1222849 + 1141.6h + (-1.39h2) = 0.0 + (1.39h2) + (-1.39h2)
1222849 + 1141.6h + (-1.39h2) = (1.39h2) + (-1.39h2)

Combine like terms: (1.39h2) + (-1.39h2) = 0.00
1222849 + 1141.6h + (-1.39h2) = 0.00

Begin completing the square.  Divide all terms by
-1.39 the coefficient of the squared term: 

Divide each side by '-1.39'.
-879747.482 + -821.294964h + h2 = 0

Move the constant term to the right:

Add '879747.482' to each side of the equation.
-879747.482 + -821.294964h + 879747.482 + h2 = 0 + 879747.482

Reorder the terms:
-879747.482 + 879747.482 + -821.294964h + h2 = 0 + 879747.482

Combine like terms: -879747.482 + 879747.482 = 0.000
0.000 + -821.294964h + h2 = 0 + 879747.482
-821.294964h + h2 = 0 + 879747.482

Combine like terms: 0 + 879747.482 = 879747.482
-821.294964h + h2 = 879747.482

The h term is -821.294964h.  Take half its coefficient (-410.647482).
Square it (168631.3545) and add it to both sides.

Add '168631.3545' to each side of the equation.
-821.294964h + 168631.3545 + h2 = 879747.482 + 168631.3545

Reorder the terms:
168631.3545 + -821.294964h + h2 = 879747.482 + 168631.3545

Combine like terms: 879747.482 + 168631.3545 = 1048378.8365
168631.3545 + -821.294964h + h2 = 1048378.8365

Factor a perfect square on the left side:
((h) + -410.647482)((h) + -410.647482) = 1048378.8365

Calculate the square root of the right side: 1023.903724234

Break this problem into two subproblems by setting 
((h) + -410.647482) equal to 1023.903724234 and -1023.903724234.

Subproblem 1

(h) + -410.647482 = 1023.903724234 Simplifying (h) + -410.647482 = 1023.903724234 h + -410.647482 = 1023.903724234 Reorder the terms: -410.647482 + h = 1023.903724234 Solving -410.647482 + h = 1023.903724234 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '410.647482' to each side of the equation. -410.647482 + 410.647482 + h = 1023.903724234 + 410.647482 Combine like terms: -410.647482 + 410.647482 = 0.000000 0.000000 + h = 1023.903724234 + 410.647482 h = 1023.903724234 + 410.647482 Combine like terms: 1023.903724234 + 410.647482 = 1434.551206234 h = 1434.551206234 Simplifying h = 1434.551206234

Subproblem 2

(h) + -410.647482 = -1023.903724234 Simplifying (h) + -410.647482 = -1023.903724234 h + -410.647482 = -1023.903724234 Reorder the terms: -410.647482 + h = -1023.903724234 Solving -410.647482 + h = -1023.903724234 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '410.647482' to each side of the equation. -410.647482 + 410.647482 + h = -1023.903724234 + 410.647482 Combine like terms: -410.647482 + 410.647482 = 0.000000 0.000000 + h = -1023.903724234 + 410.647482 h = -1023.903724234 + 410.647482 Combine like terms: -1023.903724234 + 410.647482 = -613.256242234 h = -613.256242234 Simplifying h = -613.256242234

Solution

The solution to the problem is based on the solutions from the subproblems. h = {1434.551206234, -613.256242234}

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