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Simplifying 9h2 + -50h + 53 = 0 Reorder the terms: 53 + -50h + 9h2 = 0 Solving 53 + -50h + 9h2 = 0 Solving for variable 'h'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 5.888888889 + -5.555555556h + h2 = 0 Move the constant term to the right: Add '-5.888888889' to each side of the equation. 5.888888889 + -5.555555556h + -5.888888889 + h2 = 0 + -5.888888889 Reorder the terms: 5.888888889 + -5.888888889 + -5.555555556h + h2 = 0 + -5.888888889 Combine like terms: 5.888888889 + -5.888888889 = 0.000000000 0.000000000 + -5.555555556h + h2 = 0 + -5.888888889 -5.555555556h + h2 = 0 + -5.888888889 Combine like terms: 0 + -5.888888889 = -5.888888889 -5.555555556h + h2 = -5.888888889 The h term is -5.555555556h. Take half its coefficient (-2.777777778). Square it (7.716049384) and add it to both sides. Add '7.716049384' to each side of the equation. -5.555555556h + 7.716049384 + h2 = -5.888888889 + 7.716049384 Reorder the terms: 7.716049384 + -5.555555556h + h2 = -5.888888889 + 7.716049384 Combine like terms: -5.888888889 + 7.716049384 = 1.827160495 7.716049384 + -5.555555556h + h2 = 1.827160495 Factor a perfect square on the left side: (h + -2.777777778)(h + -2.777777778) = 1.827160495 Calculate the square root of the right side: 1.351725007 Break this problem into two subproblems by setting (h + -2.777777778) equal to 1.351725007 and -1.351725007.Subproblem 1
h + -2.777777778 = 1.351725007 Simplifying h + -2.777777778 = 1.351725007 Reorder the terms: -2.777777778 + h = 1.351725007 Solving -2.777777778 + h = 1.351725007 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '2.777777778' to each side of the equation. -2.777777778 + 2.777777778 + h = 1.351725007 + 2.777777778 Combine like terms: -2.777777778 + 2.777777778 = 0.000000000 0.000000000 + h = 1.351725007 + 2.777777778 h = 1.351725007 + 2.777777778 Combine like terms: 1.351725007 + 2.777777778 = 4.129502785 h = 4.129502785 Simplifying h = 4.129502785Subproblem 2
h + -2.777777778 = -1.351725007 Simplifying h + -2.777777778 = -1.351725007 Reorder the terms: -2.777777778 + h = -1.351725007 Solving -2.777777778 + h = -1.351725007 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '2.777777778' to each side of the equation. -2.777777778 + 2.777777778 + h = -1.351725007 + 2.777777778 Combine like terms: -2.777777778 + 2.777777778 = 0.000000000 0.000000000 + h = -1.351725007 + 2.777777778 h = -1.351725007 + 2.777777778 Combine like terms: -1.351725007 + 2.777777778 = 1.426052771 h = 1.426052771 Simplifying h = 1.426052771Solution
The solution to the problem is based on the solutions from the subproblems. h = {4.129502785, 1.426052771}
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