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Simplifying 30h5 + -6h4 + -15h3 = 0 Reorder the terms: -15h3 + -6h4 + 30h5 = 0 Solving -15h3 + -6h4 + 30h5 = 0 Solving for variable 'h'. Factor out the Greatest Common Factor (GCF), '3h3'. 3h3(-5 + -2h + 10h2) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'h3' equal to zero and attempt to solve: Simplifying h3 = 0 Solving h3 = 0 Move all terms containing h to the left, all other terms to the right. Simplifying h3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-5 + -2h + 10h2)' equal to zero and attempt to solve: Simplifying -5 + -2h + 10h2 = 0 Solving -5 + -2h + 10h2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.5 + -0.2h + h2 = 0.0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -0.2h + 0.5 + h2 = 0.0 + 0.5 Reorder the terms: -0.5 + 0.5 + -0.2h + h2 = 0.0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -0.2h + h2 = 0.0 + 0.5 -0.2h + h2 = 0.0 + 0.5 Combine like terms: 0.0 + 0.5 = 0.5 -0.2h + h2 = 0.5 The h term is -0.2h. Take half its coefficient (-0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. -0.2h + 0.01 + h2 = 0.5 + 0.01 Reorder the terms: 0.01 + -0.2h + h2 = 0.5 + 0.01 Combine like terms: 0.5 + 0.01 = 0.51 0.01 + -0.2h + h2 = 0.51 Factor a perfect square on the left side: (h + -0.1)(h + -0.1) = 0.51 Calculate the square root of the right side: 0.714142843 Break this problem into two subproblems by setting (h + -0.1) equal to 0.714142843 and -0.714142843.Subproblem 1
h + -0.1 = 0.714142843 Simplifying h + -0.1 = 0.714142843 Reorder the terms: -0.1 + h = 0.714142843 Solving -0.1 + h = 0.714142843 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + h = 0.714142843 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + h = 0.714142843 + 0.1 h = 0.714142843 + 0.1 Combine like terms: 0.714142843 + 0.1 = 0.814142843 h = 0.814142843 Simplifying h = 0.814142843Subproblem 2
h + -0.1 = -0.714142843 Simplifying h + -0.1 = -0.714142843 Reorder the terms: -0.1 + h = -0.714142843 Solving -0.1 + h = -0.714142843 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + h = -0.714142843 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + h = -0.714142843 + 0.1 h = -0.714142843 + 0.1 Combine like terms: -0.714142843 + 0.1 = -0.614142843 h = -0.614142843 Simplifying h = -0.614142843Solution
The solution to the problem is based on the solutions from the subproblems. h = {0.814142843, -0.614142843}Solution
h = {0.814142843, -0.614142843}
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