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Simplifying 3h2 + -5h + -9 = 0 Reorder the terms: -9 + -5h + 3h2 = 0 Solving -9 + -5h + 3h2 = 0 Solving for variable 'h'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3 + -1.666666667h + h2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -1.666666667h + 3 + h2 = 0 + 3 Reorder the terms: -3 + 3 + -1.666666667h + h2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1.666666667h + h2 = 0 + 3 -1.666666667h + h2 = 0 + 3 Combine like terms: 0 + 3 = 3 -1.666666667h + h2 = 3 The h term is -1.666666667h. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667h + 0.6944444447 + h2 = 3 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667h + h2 = 3 + 0.6944444447 Combine like terms: 3 + 0.6944444447 = 3.6944444447 0.6944444447 + -1.666666667h + h2 = 3.6944444447 Factor a perfect square on the left side: (h + -0.8333333335)(h + -0.8333333335) = 3.6944444447 Calculate the square root of the right side: 1.922093766 Break this problem into two subproblems by setting (h + -0.8333333335) equal to 1.922093766 and -1.922093766.Subproblem 1
h + -0.8333333335 = 1.922093766 Simplifying h + -0.8333333335 = 1.922093766 Reorder the terms: -0.8333333335 + h = 1.922093766 Solving -0.8333333335 + h = 1.922093766 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + h = 1.922093766 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + h = 1.922093766 + 0.8333333335 h = 1.922093766 + 0.8333333335 Combine like terms: 1.922093766 + 0.8333333335 = 2.7554270995 h = 2.7554270995 Simplifying h = 2.7554270995Subproblem 2
h + -0.8333333335 = -1.922093766 Simplifying h + -0.8333333335 = -1.922093766 Reorder the terms: -0.8333333335 + h = -1.922093766 Solving -0.8333333335 + h = -1.922093766 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + h = -1.922093766 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + h = -1.922093766 + 0.8333333335 h = -1.922093766 + 0.8333333335 Combine like terms: -1.922093766 + 0.8333333335 = -1.0887604325 h = -1.0887604325 Simplifying h = -1.0887604325Solution
The solution to the problem is based on the solutions from the subproblems. h = {2.7554270995, -1.0887604325}
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