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Simplifying h2 + -2.5h + -1.25 = 0 Reorder the terms: -1.25 + -2.5h + h2 = 0 Solving -1.25 + -2.5h + h2 = 0 Solving for variable 'h'. Begin completing the square. Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -2.5h + 1.25 + h2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -2.5h + h2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -2.5h + h2 = 0 + 1.25 -2.5h + h2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -2.5h + h2 = 1.25 The h term is -2.5h. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5h + 1.5625 + h2 = 1.25 + 1.5625 Reorder the terms: 1.5625 + -2.5h + h2 = 1.25 + 1.5625 Combine like terms: 1.25 + 1.5625 = 2.8125 1.5625 + -2.5h + h2 = 2.8125 Factor a perfect square on the left side: (h + -1.25)(h + -1.25) = 2.8125 Calculate the square root of the right side: 1.677050983 Break this problem into two subproblems by setting (h + -1.25) equal to 1.677050983 and -1.677050983.Subproblem 1
h + -1.25 = 1.677050983 Simplifying h + -1.25 = 1.677050983 Reorder the terms: -1.25 + h = 1.677050983 Solving -1.25 + h = 1.677050983 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + h = 1.677050983 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + h = 1.677050983 + 1.25 h = 1.677050983 + 1.25 Combine like terms: 1.677050983 + 1.25 = 2.927050983 h = 2.927050983 Simplifying h = 2.927050983Subproblem 2
h + -1.25 = -1.677050983 Simplifying h + -1.25 = -1.677050983 Reorder the terms: -1.25 + h = -1.677050983 Solving -1.25 + h = -1.677050983 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + h = -1.677050983 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + h = -1.677050983 + 1.25 h = -1.677050983 + 1.25 Combine like terms: -1.677050983 + 1.25 = -0.427050983 h = -0.427050983 Simplifying h = -0.427050983Solution
The solution to the problem is based on the solutions from the subproblems. h = {2.927050983, -0.427050983}
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