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Simplifying -1h2 + 15h + 50 = 0 Reorder the terms: 50 + 15h + -1h2 = 0 Solving 50 + 15h + -1h2 = 0 Solving for variable 'h'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -50 + -15h + h2 = 0 Move the constant term to the right: Add '50' to each side of the equation. -50 + -15h + 50 + h2 = 0 + 50 Reorder the terms: -50 + 50 + -15h + h2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + -15h + h2 = 0 + 50 -15h + h2 = 0 + 50 Combine like terms: 0 + 50 = 50 -15h + h2 = 50 The h term is -15h. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15h + 56.25 + h2 = 50 + 56.25 Reorder the terms: 56.25 + -15h + h2 = 50 + 56.25 Combine like terms: 50 + 56.25 = 106.25 56.25 + -15h + h2 = 106.25 Factor a perfect square on the left side: (h + -7.5)(h + -7.5) = 106.25 Calculate the square root of the right side: 10.307764064 Break this problem into two subproblems by setting (h + -7.5) equal to 10.307764064 and -10.307764064.Subproblem 1
h + -7.5 = 10.307764064 Simplifying h + -7.5 = 10.307764064 Reorder the terms: -7.5 + h = 10.307764064 Solving -7.5 + h = 10.307764064 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + h = 10.307764064 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + h = 10.307764064 + 7.5 h = 10.307764064 + 7.5 Combine like terms: 10.307764064 + 7.5 = 17.807764064 h = 17.807764064 Simplifying h = 17.807764064Subproblem 2
h + -7.5 = -10.307764064 Simplifying h + -7.5 = -10.307764064 Reorder the terms: -7.5 + h = -10.307764064 Solving -7.5 + h = -10.307764064 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + h = -10.307764064 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + h = -10.307764064 + 7.5 h = -10.307764064 + 7.5 Combine like terms: -10.307764064 + 7.5 = -2.807764064 h = -2.807764064 Simplifying h = -2.807764064Solution
The solution to the problem is based on the solutions from the subproblems. h = {17.807764064, -2.807764064}
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