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Simplifying h2 + -2h + -1 = 24 Reorder the terms: -1 + -2h + h2 = 24 Solving -1 + -2h + h2 = 24 Solving for variable 'h'. Reorder the terms: -1 + -24 + -2h + h2 = 24 + -24 Combine like terms: -1 + -24 = -25 -25 + -2h + h2 = 24 + -24 Combine like terms: 24 + -24 = 0 -25 + -2h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + -2h + 25 + h2 = 0 + 25 Reorder the terms: -25 + 25 + -2h + h2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -2h + h2 = 0 + 25 -2h + h2 = 0 + 25 Combine like terms: 0 + 25 = 25 -2h + h2 = 25 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 = 25 + 1 Reorder the terms: 1 + -2h + h2 = 25 + 1 Combine like terms: 25 + 1 = 26 1 + -2h + h2 = 26 Factor a perfect square on the left side: (h + -1)(h + -1) = 26 Calculate the square root of the right side: 5.099019514 Break this problem into two subproblems by setting (h + -1) equal to 5.099019514 and -5.099019514.Subproblem 1
h + -1 = 5.099019514 Simplifying h + -1 = 5.099019514 Reorder the terms: -1 + h = 5.099019514 Solving -1 + h = 5.099019514 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 = 5.099019514 + 1 Combine like terms: -1 + 1 = 0 0 + h = 5.099019514 + 1 h = 5.099019514 + 1 Combine like terms: 5.099019514 + 1 = 6.099019514 h = 6.099019514 Simplifying h = 6.099019514Subproblem 2
h + -1 = -5.099019514 Simplifying h + -1 = -5.099019514 Reorder the terms: -1 + h = -5.099019514 Solving -1 + h = -5.099019514 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 = -5.099019514 + 1 Combine like terms: -1 + 1 = 0 0 + h = -5.099019514 + 1 h = -5.099019514 + 1 Combine like terms: -5.099019514 + 1 = -4.099019514 h = -4.099019514 Simplifying h = -4.099019514Solution
The solution to the problem is based on the solutions from the subproblems. h = {6.099019514, -4.099019514}
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