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Simplifying 7h2 + -23h + -6 = 0 Reorder the terms: -6 + -23h + 7h2 = 0 Solving -6 + -23h + 7h2 = 0 Solving for variable 'h'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.8571428571 + -3.285714286h + h2 = 0 Move the constant term to the right: Add '0.8571428571' to each side of the equation. -0.8571428571 + -3.285714286h + 0.8571428571 + h2 = 0 + 0.8571428571 Reorder the terms: -0.8571428571 + 0.8571428571 + -3.285714286h + h2 = 0 + 0.8571428571 Combine like terms: -0.8571428571 + 0.8571428571 = 0.0000000000 0.0000000000 + -3.285714286h + h2 = 0 + 0.8571428571 -3.285714286h + h2 = 0 + 0.8571428571 Combine like terms: 0 + 0.8571428571 = 0.8571428571 -3.285714286h + h2 = 0.8571428571 The h term is -3.285714286h. Take half its coefficient (-1.642857143). Square it (2.698979592) and add it to both sides. Add '2.698979592' to each side of the equation. -3.285714286h + 2.698979592 + h2 = 0.8571428571 + 2.698979592 Reorder the terms: 2.698979592 + -3.285714286h + h2 = 0.8571428571 + 2.698979592 Combine like terms: 0.8571428571 + 2.698979592 = 3.5561224491 2.698979592 + -3.285714286h + h2 = 3.5561224491 Factor a perfect square on the left side: (h + -1.642857143)(h + -1.642857143) = 3.5561224491 Calculate the square root of the right side: 1.885768398 Break this problem into two subproblems by setting (h + -1.642857143) equal to 1.885768398 and -1.885768398.Subproblem 1
h + -1.642857143 = 1.885768398 Simplifying h + -1.642857143 = 1.885768398 Reorder the terms: -1.642857143 + h = 1.885768398 Solving -1.642857143 + h = 1.885768398 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '1.642857143' to each side of the equation. -1.642857143 + 1.642857143 + h = 1.885768398 + 1.642857143 Combine like terms: -1.642857143 + 1.642857143 = 0.000000000 0.000000000 + h = 1.885768398 + 1.642857143 h = 1.885768398 + 1.642857143 Combine like terms: 1.885768398 + 1.642857143 = 3.528625541 h = 3.528625541 Simplifying h = 3.528625541Subproblem 2
h + -1.642857143 = -1.885768398 Simplifying h + -1.642857143 = -1.885768398 Reorder the terms: -1.642857143 + h = -1.885768398 Solving -1.642857143 + h = -1.885768398 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '1.642857143' to each side of the equation. -1.642857143 + 1.642857143 + h = -1.885768398 + 1.642857143 Combine like terms: -1.642857143 + 1.642857143 = 0.000000000 0.000000000 + h = -1.885768398 + 1.642857143 h = -1.885768398 + 1.642857143 Combine like terms: -1.885768398 + 1.642857143 = -0.242911255 h = -0.242911255 Simplifying h = -0.242911255Solution
The solution to the problem is based on the solutions from the subproblems. h = {3.528625541, -0.242911255}
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