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Simplifying 350h2 + -58.8h + -0.3888 = 0 Reorder the terms: -0.3888 + -58.8h + 350h2 = 0 Solving -0.3888 + -58.8h + 350h2 = 0 Solving for variable 'h'. Begin completing the square. Divide all terms by 350 the coefficient of the squared term: Divide each side by '350'. -0.001110857143 + -0.168h + h2 = 0 Move the constant term to the right: Add '0.001110857143' to each side of the equation. -0.001110857143 + -0.168h + 0.001110857143 + h2 = 0 + 0.001110857143 Reorder the terms: -0.001110857143 + 0.001110857143 + -0.168h + h2 = 0 + 0.001110857143 Combine like terms: -0.001110857143 + 0.001110857143 = 0.000000000000 0.000000000000 + -0.168h + h2 = 0 + 0.001110857143 -0.168h + h2 = 0 + 0.001110857143 Combine like terms: 0 + 0.001110857143 = 0.001110857143 -0.168h + h2 = 0.001110857143 The h term is -0.168h. Take half its coefficient (-0.084). Square it (0.007056) and add it to both sides. Add '0.007056' to each side of the equation. -0.168h + 0.007056 + h2 = 0.001110857143 + 0.007056 Reorder the terms: 0.007056 + -0.168h + h2 = 0.001110857143 + 0.007056 Combine like terms: 0.001110857143 + 0.007056 = 0.008166857143 0.007056 + -0.168h + h2 = 0.008166857143 Factor a perfect square on the left side: (h + -0.084)(h + -0.084) = 0.008166857143 Calculate the square root of the right side: 0.090370665 Break this problem into two subproblems by setting (h + -0.084) equal to 0.090370665 and -0.090370665.Subproblem 1
h + -0.084 = 0.090370665 Simplifying h + -0.084 = 0.090370665 Reorder the terms: -0.084 + h = 0.090370665 Solving -0.084 + h = 0.090370665 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '0.084' to each side of the equation. -0.084 + 0.084 + h = 0.090370665 + 0.084 Combine like terms: -0.084 + 0.084 = 0.000 0.000 + h = 0.090370665 + 0.084 h = 0.090370665 + 0.084 Combine like terms: 0.090370665 + 0.084 = 0.174370665 h = 0.174370665 Simplifying h = 0.174370665Subproblem 2
h + -0.084 = -0.090370665 Simplifying h + -0.084 = -0.090370665 Reorder the terms: -0.084 + h = -0.090370665 Solving -0.084 + h = -0.090370665 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '0.084' to each side of the equation. -0.084 + 0.084 + h = -0.090370665 + 0.084 Combine like terms: -0.084 + 0.084 = 0.000 0.000 + h = -0.090370665 + 0.084 h = -0.090370665 + 0.084 Combine like terms: -0.090370665 + 0.084 = -0.006370665 h = -0.006370665 Simplifying h = -0.006370665Solution
The solution to the problem is based on the solutions from the subproblems. h = {0.174370665, -0.006370665}
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