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Simplifying 46h = 4h3 + 5h2 Reorder the terms: 46h = 5h2 + 4h3 Solving 46h = 5h2 + 4h3 Solving for variable 'h'. Reorder the terms: 46h + -5h2 + -4h3 = 5h2 + -5h2 + 4h3 + -4h3 Combine like terms: 5h2 + -5h2 = 0 46h + -5h2 + -4h3 = 0 + 4h3 + -4h3 46h + -5h2 + -4h3 = 4h3 + -4h3 Combine like terms: 4h3 + -4h3 = 0 46h + -5h2 + -4h3 = 0 Factor out the Greatest Common Factor (GCF), 'h'. h(46 + -5h + -4h2) = 0Subproblem 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 '(46 + -5h + -4h2)' equal to zero and attempt to solve: Simplifying 46 + -5h + -4h2 = 0 Solving 46 + -5h + -4h2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -11.5 + 1.25h + h2 = 0 Move the constant term to the right: Add '11.5' to each side of the equation. -11.5 + 1.25h + 11.5 + h2 = 0 + 11.5 Reorder the terms: -11.5 + 11.5 + 1.25h + h2 = 0 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + 1.25h + h2 = 0 + 11.5 1.25h + h2 = 0 + 11.5 Combine like terms: 0 + 11.5 = 11.5 1.25h + h2 = 11.5 The h term is 1.25h. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25h + 0.390625 + h2 = 11.5 + 0.390625 Reorder the terms: 0.390625 + 1.25h + h2 = 11.5 + 0.390625 Combine like terms: 11.5 + 0.390625 = 11.890625 0.390625 + 1.25h + h2 = 11.890625 Factor a perfect square on the left side: (h + 0.625)(h + 0.625) = 11.890625 Calculate the square root of the right side: 3.448278556 Break this problem into two subproblems by setting (h + 0.625) equal to 3.448278556 and -3.448278556.Subproblem 1
h + 0.625 = 3.448278556 Simplifying h + 0.625 = 3.448278556 Reorder the terms: 0.625 + h = 3.448278556 Solving 0.625 + h = 3.448278556 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + h = 3.448278556 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + h = 3.448278556 + -0.625 h = 3.448278556 + -0.625 Combine like terms: 3.448278556 + -0.625 = 2.823278556 h = 2.823278556 Simplifying h = 2.823278556Subproblem 2
h + 0.625 = -3.448278556 Simplifying h + 0.625 = -3.448278556 Reorder the terms: 0.625 + h = -3.448278556 Solving 0.625 + h = -3.448278556 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + h = -3.448278556 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + h = -3.448278556 + -0.625 h = -3.448278556 + -0.625 Combine like terms: -3.448278556 + -0.625 = -4.073278556 h = -4.073278556 Simplifying h = -4.073278556Solution
The solution to the problem is based on the solutions from the subproblems. h = {2.823278556, -4.073278556}Solution
h = {0, 2.823278556, -4.073278556}
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