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Simplifying 0 = -15 + 29h + 12h2 Solving 0 = -15 + 29h + 12h2 Solving for variable 'h'. Combine like terms: 0 + 15 = 15 15 + -29h + -12h2 = -15 + 29h + 12h2 + 15 + -29h + -12h2 Reorder the terms: 15 + -29h + -12h2 = -15 + 15 + 29h + -29h + 12h2 + -12h2 Combine like terms: -15 + 15 = 0 15 + -29h + -12h2 = 0 + 29h + -29h + 12h2 + -12h2 15 + -29h + -12h2 = 29h + -29h + 12h2 + -12h2 Combine like terms: 29h + -29h = 0 15 + -29h + -12h2 = 0 + 12h2 + -12h2 15 + -29h + -12h2 = 12h2 + -12h2 Combine like terms: 12h2 + -12h2 = 0 15 + -29h + -12h2 = 0 Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. -1.25 + 2.416666667h + h2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + 2.416666667h + 1.25 + h2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + 2.416666667h + h2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + 2.416666667h + h2 = 0 + 1.25 2.416666667h + h2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 2.416666667h + h2 = 1.25 The h term is 2.416666667h. Take half its coefficient (1.208333334). Square it (1.460069446) and add it to both sides. Add '1.460069446' to each side of the equation. 2.416666667h + 1.460069446 + h2 = 1.25 + 1.460069446 Reorder the terms: 1.460069446 + 2.416666667h + h2 = 1.25 + 1.460069446 Combine like terms: 1.25 + 1.460069446 = 2.710069446 1.460069446 + 2.416666667h + h2 = 2.710069446 Factor a perfect square on the left side: (h + 1.208333334)(h + 1.208333334) = 2.710069446 Calculate the square root of the right side: 1.646228856 Break this problem into two subproblems by setting (h + 1.208333334) equal to 1.646228856 and -1.646228856.Subproblem 1
h + 1.208333334 = 1.646228856 Simplifying h + 1.208333334 = 1.646228856 Reorder the terms: 1.208333334 + h = 1.646228856 Solving 1.208333334 + h = 1.646228856 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-1.208333334' to each side of the equation. 1.208333334 + -1.208333334 + h = 1.646228856 + -1.208333334 Combine like terms: 1.208333334 + -1.208333334 = 0.000000000 0.000000000 + h = 1.646228856 + -1.208333334 h = 1.646228856 + -1.208333334 Combine like terms: 1.646228856 + -1.208333334 = 0.437895522 h = 0.437895522 Simplifying h = 0.437895522Subproblem 2
h + 1.208333334 = -1.646228856 Simplifying h + 1.208333334 = -1.646228856 Reorder the terms: 1.208333334 + h = -1.646228856 Solving 1.208333334 + h = -1.646228856 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-1.208333334' to each side of the equation. 1.208333334 + -1.208333334 + h = -1.646228856 + -1.208333334 Combine like terms: 1.208333334 + -1.208333334 = 0.000000000 0.000000000 + h = -1.646228856 + -1.208333334 h = -1.646228856 + -1.208333334 Combine like terms: -1.646228856 + -1.208333334 = -2.85456219 h = -2.85456219 Simplifying h = -2.85456219Solution
The solution to the problem is based on the solutions from the subproblems. h = {0.437895522, -2.85456219}
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