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Simplifying 36h2 + 14h + -19h2 + 11h + 5 + 4 = 0 Reorder the terms: 5 + 4 + 14h + 11h + 36h2 + -19h2 = 0 Combine like terms: 5 + 4 = 9 9 + 14h + 11h + 36h2 + -19h2 = 0 Combine like terms: 14h + 11h = 25h 9 + 25h + 36h2 + -19h2 = 0 Combine like terms: 36h2 + -19h2 = 17h2 9 + 25h + 17h2 = 0 Solving 9 + 25h + 17h2 = 0 Solving for variable 'h'. Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. 0.5294117647 + 1.470588235h + h2 = 0 Move the constant term to the right: Add '-0.5294117647' to each side of the equation. 0.5294117647 + 1.470588235h + -0.5294117647 + h2 = 0 + -0.5294117647 Reorder the terms: 0.5294117647 + -0.5294117647 + 1.470588235h + h2 = 0 + -0.5294117647 Combine like terms: 0.5294117647 + -0.5294117647 = 0.0000000000 0.0000000000 + 1.470588235h + h2 = 0 + -0.5294117647 1.470588235h + h2 = 0 + -0.5294117647 Combine like terms: 0 + -0.5294117647 = -0.5294117647 1.470588235h + h2 = -0.5294117647 The h term is 1.470588235h. Take half its coefficient (0.7352941175). Square it (0.5406574392) and add it to both sides. Add '0.5406574392' to each side of the equation. 1.470588235h + 0.5406574392 + h2 = -0.5294117647 + 0.5406574392 Reorder the terms: 0.5406574392 + 1.470588235h + h2 = -0.5294117647 + 0.5406574392 Combine like terms: -0.5294117647 + 0.5406574392 = 0.0112456745 0.5406574392 + 1.470588235h + h2 = 0.0112456745 Factor a perfect square on the left side: (h + 0.7352941175)(h + 0.7352941175) = 0.0112456745 Calculate the square root of the right side: 0.106045625 Break this problem into two subproblems by setting (h + 0.7352941175) equal to 0.106045625 and -0.106045625.Subproblem 1
h + 0.7352941175 = 0.106045625 Simplifying h + 0.7352941175 = 0.106045625 Reorder the terms: 0.7352941175 + h = 0.106045625 Solving 0.7352941175 + h = 0.106045625 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-0.7352941175' to each side of the equation. 0.7352941175 + -0.7352941175 + h = 0.106045625 + -0.7352941175 Combine like terms: 0.7352941175 + -0.7352941175 = 0.0000000000 0.0000000000 + h = 0.106045625 + -0.7352941175 h = 0.106045625 + -0.7352941175 Combine like terms: 0.106045625 + -0.7352941175 = -0.6292484925 h = -0.6292484925 Simplifying h = -0.6292484925Subproblem 2
h + 0.7352941175 = -0.106045625 Simplifying h + 0.7352941175 = -0.106045625 Reorder the terms: 0.7352941175 + h = -0.106045625 Solving 0.7352941175 + h = -0.106045625 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-0.7352941175' to each side of the equation. 0.7352941175 + -0.7352941175 + h = -0.106045625 + -0.7352941175 Combine like terms: 0.7352941175 + -0.7352941175 = 0.0000000000 0.0000000000 + h = -0.106045625 + -0.7352941175 h = -0.106045625 + -0.7352941175 Combine like terms: -0.106045625 + -0.7352941175 = -0.8413397425 h = -0.8413397425 Simplifying h = -0.8413397425Solution
The solution to the problem is based on the solutions from the subproblems. h = {-0.6292484925, -0.8413397425}
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