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Simplifying 21h3 + 35h2 + -28h = 0 Reorder the terms: -28h + 35h2 + 21h3 = 0 Solving -28h + 35h2 + 21h3 = 0 Solving for variable 'h'. Factor out the Greatest Common Factor (GCF), '7h'. 7h(-4 + 5h + 3h2) = 0 Ignore the factor 7.Subproblem 1
Set the factor 'h' equal to zero and attempt to solve: Simplifying h = 0 Solving h = 0 Move all terms containing h to the left, all other terms to the right. Simplifying h = 0Subproblem 2
Set the factor '(-4 + 5h + 3h2)' equal to zero and attempt to solve: Simplifying -4 + 5h + 3h2 = 0 Solving -4 + 5h + 3h2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1.333333333 + 1.666666667h + h2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + 1.666666667h + 1.333333333 + h2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + 1.666666667h + h2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + 1.666666667h + h2 = 0 + 1.333333333 1.666666667h + h2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 1.666666667h + h2 = 1.333333333 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 = 1.333333333 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667h + h2 = 1.333333333 + 0.6944444447 Combine like terms: 1.333333333 + 0.6944444447 = 2.0277777777 0.6944444447 + 1.666666667h + h2 = 2.0277777777 Factor a perfect square on the left side: (h + 0.8333333335)(h + 0.8333333335) = 2.0277777777 Calculate the square root of the right side: 1.424000624 Break this problem into two subproblems by setting (h + 0.8333333335) equal to 1.424000624 and -1.424000624.Subproblem 1
h + 0.8333333335 = 1.424000624 Simplifying h + 0.8333333335 = 1.424000624 Reorder the terms: 0.8333333335 + h = 1.424000624 Solving 0.8333333335 + h = 1.424000624 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 = 1.424000624 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + h = 1.424000624 + -0.8333333335 h = 1.424000624 + -0.8333333335 Combine like terms: 1.424000624 + -0.8333333335 = 0.5906672905 h = 0.5906672905 Simplifying h = 0.5906672905Subproblem 2
h + 0.8333333335 = -1.424000624 Simplifying h + 0.8333333335 = -1.424000624 Reorder the terms: 0.8333333335 + h = -1.424000624 Solving 0.8333333335 + h = -1.424000624 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 = -1.424000624 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + h = -1.424000624 + -0.8333333335 h = -1.424000624 + -0.8333333335 Combine like terms: -1.424000624 + -0.8333333335 = -2.2573339575 h = -2.2573339575 Simplifying h = -2.2573339575Solution
The solution to the problem is based on the solutions from the subproblems. h = {0.5906672905, -2.2573339575}Solution
h = {0, 0.5906672905, -2.2573339575}
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