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Simplifying 200 + -7000h2 = 100h Solving 200 + -7000h2 = 100h Solving for variable 'h'. Reorder the terms: 200 + -100h + -7000h2 = 100h + -100h Combine like terms: 100h + -100h = 0 200 + -100h + -7000h2 = 0 Factor out the Greatest Common Factor (GCF), '100'. 100(2 + -1h + -70h2) = 0 Ignore the factor 100.Subproblem 1
Set the factor '(2 + -1h + -70h2)' equal to zero and attempt to solve: Simplifying 2 + -1h + -70h2 = 0 Solving 2 + -1h + -70h2 = 0 Begin completing the square. Divide all terms by -70 the coefficient of the squared term: Divide each side by '-70'. -0.02857142857 + 0.01428571429h + h2 = 0.0 Move the constant term to the right: Add '0.02857142857' to each side of the equation. -0.02857142857 + 0.01428571429h + 0.02857142857 + h2 = 0.0 + 0.02857142857 Reorder the terms: -0.02857142857 + 0.02857142857 + 0.01428571429h + h2 = 0.0 + 0.02857142857 Combine like terms: -0.02857142857 + 0.02857142857 = 0.00000000000 0.00000000000 + 0.01428571429h + h2 = 0.0 + 0.02857142857 0.01428571429h + h2 = 0.0 + 0.02857142857 Combine like terms: 0.0 + 0.02857142857 = 0.02857142857 0.01428571429h + h2 = 0.02857142857 The h term is 0.01428571429h. Take half its coefficient (0.007142857145). Square it (0.00005102040819) and add it to both sides. Add '0.00005102040819' to each side of the equation. 0.01428571429h + 0.00005102040819 + h2 = 0.02857142857 + 0.00005102040819 Reorder the terms: 0.00005102040819 + 0.01428571429h + h2 = 0.02857142857 + 0.00005102040819 Combine like terms: 0.02857142857 + 0.00005102040819 = 0.02862244897819 0.00005102040819 + 0.01428571429h + h2 = 0.02862244897819 Factor a perfect square on the left side: (h + 0.007142857145)(h + 0.007142857145) = 0.02862244897819 Calculate the square root of the right side: 0.169181704 Break this problem into two subproblems by setting (h + 0.007142857145) equal to 0.169181704 and -0.169181704.Subproblem 1
h + 0.007142857145 = 0.169181704 Simplifying h + 0.007142857145 = 0.169181704 Reorder the terms: 0.007142857145 + h = 0.169181704 Solving 0.007142857145 + h = 0.169181704 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-0.007142857145' to each side of the equation. 0.007142857145 + -0.007142857145 + h = 0.169181704 + -0.007142857145 Combine like terms: 0.007142857145 + -0.007142857145 = 0.000000000000 0.000000000000 + h = 0.169181704 + -0.007142857145 h = 0.169181704 + -0.007142857145 Combine like terms: 0.169181704 + -0.007142857145 = 0.162038846855 h = 0.162038846855 Simplifying h = 0.162038846855Subproblem 2
h + 0.007142857145 = -0.169181704 Simplifying h + 0.007142857145 = -0.169181704 Reorder the terms: 0.007142857145 + h = -0.169181704 Solving 0.007142857145 + h = -0.169181704 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-0.007142857145' to each side of the equation. 0.007142857145 + -0.007142857145 + h = -0.169181704 + -0.007142857145 Combine like terms: 0.007142857145 + -0.007142857145 = 0.000000000000 0.000000000000 + h = -0.169181704 + -0.007142857145 h = -0.169181704 + -0.007142857145 Combine like terms: -0.169181704 + -0.007142857145 = -0.176324561145 h = -0.176324561145 Simplifying h = -0.176324561145Solution
The solution to the problem is based on the solutions from the subproblems. h = {0.162038846855, -0.176324561145}Solution
h = {0.162038846855, -0.176324561145}
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