7h^2-38h+3=0

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Solution for 7h^2-38h+3=0 equation:


Simplifying
7h2 + -38h + 3 = 0

Reorder the terms:
3 + -38h + 7h2 = 0

Solving
3 + -38h + 7h2 = 0

Solving for variable 'h'.

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

Divide each side by '7'.
0.4285714286 + -5.428571429h + h2 = 0

Move the constant term to the right:

Add '-0.4285714286' to each side of the equation.
0.4285714286 + -5.428571429h + -0.4285714286 + h2 = 0 + -0.4285714286

Reorder the terms:
0.4285714286 + -0.4285714286 + -5.428571429h + h2 = 0 + -0.4285714286

Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000
0.0000000000 + -5.428571429h + h2 = 0 + -0.4285714286
-5.428571429h + h2 = 0 + -0.4285714286

Combine like terms: 0 + -0.4285714286 = -0.4285714286
-5.428571429h + h2 = -0.4285714286

The h term is -5.428571429h.  Take half its coefficient (-2.714285715).
Square it (7.367346943) and add it to both sides.

Add '7.367346943' to each side of the equation.
-5.428571429h + 7.367346943 + h2 = -0.4285714286 + 7.367346943

Reorder the terms:
7.367346943 + -5.428571429h + h2 = -0.4285714286 + 7.367346943

Combine like terms: -0.4285714286 + 7.367346943 = 6.9387755144
7.367346943 + -5.428571429h + h2 = 6.9387755144

Factor a perfect square on the left side:
(h + -2.714285715)(h + -2.714285715) = 6.9387755144

Calculate the square root of the right side: 2.63415556

Break this problem into two subproblems by setting 
(h + -2.714285715) equal to 2.63415556 and -2.63415556.

Subproblem 1

h + -2.714285715 = 2.63415556 Simplifying h + -2.714285715 = 2.63415556 Reorder the terms: -2.714285715 + h = 2.63415556 Solving -2.714285715 + h = 2.63415556 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '2.714285715' to each side of the equation. -2.714285715 + 2.714285715 + h = 2.63415556 + 2.714285715 Combine like terms: -2.714285715 + 2.714285715 = 0.000000000 0.000000000 + h = 2.63415556 + 2.714285715 h = 2.63415556 + 2.714285715 Combine like terms: 2.63415556 + 2.714285715 = 5.348441275 h = 5.348441275 Simplifying h = 5.348441275

Subproblem 2

h + -2.714285715 = -2.63415556 Simplifying h + -2.714285715 = -2.63415556 Reorder the terms: -2.714285715 + h = -2.63415556 Solving -2.714285715 + h = -2.63415556 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '2.714285715' to each side of the equation. -2.714285715 + 2.714285715 + h = -2.63415556 + 2.714285715 Combine like terms: -2.714285715 + 2.714285715 = 0.000000000 0.000000000 + h = -2.63415556 + 2.714285715 h = -2.63415556 + 2.714285715 Combine like terms: -2.63415556 + 2.714285715 = 0.080130155 h = 0.080130155 Simplifying h = 0.080130155

Solution

The solution to the problem is based on the solutions from the subproblems. h = {5.348441275, 0.080130155}

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