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Simplifying 54h2 + 7h + -21 = 0 Reorder the terms: -21 + 7h + 54h2 = 0 Solving -21 + 7h + 54h2 = 0 Solving for variable 'h'. Begin completing the square. Divide all terms by 54 the coefficient of the squared term: Divide each side by '54'. -0.3888888889 + 0.1296296296h + h2 = 0 Move the constant term to the right: Add '0.3888888889' to each side of the equation. -0.3888888889 + 0.1296296296h + 0.3888888889 + h2 = 0 + 0.3888888889 Reorder the terms: -0.3888888889 + 0.3888888889 + 0.1296296296h + h2 = 0 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + 0.1296296296h + h2 = 0 + 0.3888888889 0.1296296296h + h2 = 0 + 0.3888888889 Combine like terms: 0 + 0.3888888889 = 0.3888888889 0.1296296296h + h2 = 0.3888888889 The h term is 0.1296296296h. Take half its coefficient (0.0648148148). Square it (0.004200960218) and add it to both sides. Add '0.004200960218' to each side of the equation. 0.1296296296h + 0.004200960218 + h2 = 0.3888888889 + 0.004200960218 Reorder the terms: 0.004200960218 + 0.1296296296h + h2 = 0.3888888889 + 0.004200960218 Combine like terms: 0.3888888889 + 0.004200960218 = 0.393089849118 0.004200960218 + 0.1296296296h + h2 = 0.393089849118 Factor a perfect square on the left side: (h + 0.0648148148)(h + 0.0648148148) = 0.393089849118 Calculate the square root of the right side: 0.626968778 Break this problem into two subproblems by setting (h + 0.0648148148) equal to 0.626968778 and -0.626968778.Subproblem 1
h + 0.0648148148 = 0.626968778 Simplifying h + 0.0648148148 = 0.626968778 Reorder the terms: 0.0648148148 + h = 0.626968778 Solving 0.0648148148 + h = 0.626968778 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-0.0648148148' to each side of the equation. 0.0648148148 + -0.0648148148 + h = 0.626968778 + -0.0648148148 Combine like terms: 0.0648148148 + -0.0648148148 = 0.0000000000 0.0000000000 + h = 0.626968778 + -0.0648148148 h = 0.626968778 + -0.0648148148 Combine like terms: 0.626968778 + -0.0648148148 = 0.5621539632 h = 0.5621539632 Simplifying h = 0.5621539632Subproblem 2
h + 0.0648148148 = -0.626968778 Simplifying h + 0.0648148148 = -0.626968778 Reorder the terms: 0.0648148148 + h = -0.626968778 Solving 0.0648148148 + h = -0.626968778 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-0.0648148148' to each side of the equation. 0.0648148148 + -0.0648148148 + h = -0.626968778 + -0.0648148148 Combine like terms: 0.0648148148 + -0.0648148148 = 0.0000000000 0.0000000000 + h = -0.626968778 + -0.0648148148 h = -0.626968778 + -0.0648148148 Combine like terms: -0.626968778 + -0.0648148148 = -0.6917835928 h = -0.6917835928 Simplifying h = -0.6917835928Solution
The solution to the problem is based on the solutions from the subproblems. h = {0.5621539632, -0.6917835928}
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