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Simplifying 2h2 + 4h + 4 = 576 Reorder the terms: 4 + 4h + 2h2 = 576 Solving 4 + 4h + 2h2 = 576 Solving for variable 'h'. Reorder the terms: 4 + -576 + 4h + 2h2 = 576 + -576 Combine like terms: 4 + -576 = -572 -572 + 4h + 2h2 = 576 + -576 Combine like terms: 576 + -576 = 0 -572 + 4h + 2h2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-286 + 2h + h2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-286 + 2h + h2)' equal to zero and attempt to solve: Simplifying -286 + 2h + h2 = 0 Solving -286 + 2h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '286' to each side of the equation. -286 + 2h + 286 + h2 = 0 + 286 Reorder the terms: -286 + 286 + 2h + h2 = 0 + 286 Combine like terms: -286 + 286 = 0 0 + 2h + h2 = 0 + 286 2h + h2 = 0 + 286 Combine like terms: 0 + 286 = 286 2h + h2 = 286 The h term is 2h. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2h + 1 + h2 = 286 + 1 Reorder the terms: 1 + 2h + h2 = 286 + 1 Combine like terms: 286 + 1 = 287 1 + 2h + h2 = 287 Factor a perfect square on the left side: (h + 1)(h + 1) = 287 Calculate the square root of the right side: 16.941074346 Break this problem into two subproblems by setting (h + 1) equal to 16.941074346 and -16.941074346.Subproblem 1
h + 1 = 16.941074346 Simplifying h + 1 = 16.941074346 Reorder the terms: 1 + h = 16.941074346 Solving 1 + h = 16.941074346 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + h = 16.941074346 + -1 Combine like terms: 1 + -1 = 0 0 + h = 16.941074346 + -1 h = 16.941074346 + -1 Combine like terms: 16.941074346 + -1 = 15.941074346 h = 15.941074346 Simplifying h = 15.941074346Subproblem 2
h + 1 = -16.941074346 Simplifying h + 1 = -16.941074346 Reorder the terms: 1 + h = -16.941074346 Solving 1 + h = -16.941074346 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + h = -16.941074346 + -1 Combine like terms: 1 + -1 = 0 0 + h = -16.941074346 + -1 h = -16.941074346 + -1 Combine like terms: -16.941074346 + -1 = -17.941074346 h = -17.941074346 Simplifying h = -17.941074346Solution
The solution to the problem is based on the solutions from the subproblems. h = {15.941074346, -17.941074346}Solution
h = {15.941074346, -17.941074346}
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