19=-4h(h+5)+h

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Solution for 19=-4h(h+5)+h equation:


Simplifying
19 = -4h(h + 5) + h

Reorder the terms:
19 = -4h(5 + h) + h
19 = (5 * -4h + h * -4h) + h
19 = (-20h + -4h2) + h

Reorder the terms:
19 = -20h + h + -4h2

Combine like terms: -20h + h = -19h
19 = -19h + -4h2

Solving
19 = -19h + -4h2

Solving for variable 'h'.

Reorder the terms:
19 + 19h + 4h2 = -19h + 19h + -4h2 + 4h2

Combine like terms: -19h + 19h = 0
19 + 19h + 4h2 = 0 + -4h2 + 4h2
19 + 19h + 4h2 = -4h2 + 4h2

Combine like terms: -4h2 + 4h2 = 0
19 + 19h + 4h2 = 0

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

Divide each side by '4'.
4.75 + 4.75h + h2 = 0

Move the constant term to the right:

Add '-4.75' to each side of the equation.
4.75 + 4.75h + -4.75 + h2 = 0 + -4.75

Reorder the terms:
4.75 + -4.75 + 4.75h + h2 = 0 + -4.75

Combine like terms: 4.75 + -4.75 = 0.00
0.00 + 4.75h + h2 = 0 + -4.75
4.75h + h2 = 0 + -4.75

Combine like terms: 0 + -4.75 = -4.75
4.75h + h2 = -4.75

The h term is 4.75h.  Take half its coefficient (2.375).
Square it (5.640625) and add it to both sides.

Add '5.640625' to each side of the equation.
4.75h + 5.640625 + h2 = -4.75 + 5.640625

Reorder the terms:
5.640625 + 4.75h + h2 = -4.75 + 5.640625

Combine like terms: -4.75 + 5.640625 = 0.890625
5.640625 + 4.75h + h2 = 0.890625

Factor a perfect square on the left side:
(h + 2.375)(h + 2.375) = 0.890625

Calculate the square root of the right side: 0.943729304

Break this problem into two subproblems by setting 
(h + 2.375) equal to 0.943729304 and -0.943729304.

Subproblem 1

h + 2.375 = 0.943729304 Simplifying h + 2.375 = 0.943729304 Reorder the terms: 2.375 + h = 0.943729304 Solving 2.375 + h = 0.943729304 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-2.375' to each side of the equation. 2.375 + -2.375 + h = 0.943729304 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + h = 0.943729304 + -2.375 h = 0.943729304 + -2.375 Combine like terms: 0.943729304 + -2.375 = -1.431270696 h = -1.431270696 Simplifying h = -1.431270696

Subproblem 2

h + 2.375 = -0.943729304 Simplifying h + 2.375 = -0.943729304 Reorder the terms: 2.375 + h = -0.943729304 Solving 2.375 + h = -0.943729304 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-2.375' to each side of the equation. 2.375 + -2.375 + h = -0.943729304 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + h = -0.943729304 + -2.375 h = -0.943729304 + -2.375 Combine like terms: -0.943729304 + -2.375 = -3.318729304 h = -3.318729304 Simplifying h = -3.318729304

Solution

The solution to the problem is based on the solutions from the subproblems. h = {-1.431270696, -3.318729304}

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