h^2+14h+3=15

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Solution for h^2+14h+3=15 equation:


Simplifying
h2 + 14h + 3 = 15

Reorder the terms:
3 + 14h + h2 = 15

Solving
3 + 14h + h2 = 15

Solving for variable 'h'.

Reorder the terms:
3 + -15 + 14h + h2 = 15 + -15

Combine like terms: 3 + -15 = -12
-12 + 14h + h2 = 15 + -15

Combine like terms: 15 + -15 = 0
-12 + 14h + h2 = 0

Begin completing the square.

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + 14h + 12 + h2 = 0 + 12

Reorder the terms:
-12 + 12 + 14h + h2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + 14h + h2 = 0 + 12
14h + h2 = 0 + 12

Combine like terms: 0 + 12 = 12
14h + h2 = 12

The h term is 14h.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14h + 49 + h2 = 12 + 49

Reorder the terms:
49 + 14h + h2 = 12 + 49

Combine like terms: 12 + 49 = 61
49 + 14h + h2 = 61

Factor a perfect square on the left side:
(h + 7)(h + 7) = 61

Calculate the square root of the right side: 7.810249676

Break this problem into two subproblems by setting 
(h + 7) equal to 7.810249676 and -7.810249676.

Subproblem 1

h + 7 = 7.810249676 Simplifying h + 7 = 7.810249676 Reorder the terms: 7 + h = 7.810249676 Solving 7 + h = 7.810249676 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + h = 7.810249676 + -7 Combine like terms: 7 + -7 = 0 0 + h = 7.810249676 + -7 h = 7.810249676 + -7 Combine like terms: 7.810249676 + -7 = 0.810249676 h = 0.810249676 Simplifying h = 0.810249676

Subproblem 2

h + 7 = -7.810249676 Simplifying h + 7 = -7.810249676 Reorder the terms: 7 + h = -7.810249676 Solving 7 + h = -7.810249676 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + h = -7.810249676 + -7 Combine like terms: 7 + -7 = 0 0 + h = -7.810249676 + -7 h = -7.810249676 + -7 Combine like terms: -7.810249676 + -7 = -14.810249676 h = -14.810249676 Simplifying h = -14.810249676

Solution

The solution to the problem is based on the solutions from the subproblems. h = {0.810249676, -14.810249676}

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