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Simplifying 12h2 + -29h + -15 = 0 Reorder the terms: -15 + -29h + 12h2 = 0 Solving -15 + -29h + 12h2 = 0 Solving for variable 'h'. 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 = 2.85456219 h = 2.85456219 Simplifying h = 2.85456219Subproblem 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 = -0.437895522 h = -0.437895522 Simplifying h = -0.437895522Solution
The solution to the problem is based on the solutions from the subproblems. h = {2.85456219, -0.437895522}
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