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Simplifying 5h(32h + 4) = 10 Reorder the terms: 5h(4 + 32h) = 10 (4 * 5h + 32h * 5h) = 10 (20h + 160h2) = 10 Solving 20h + 160h2 = 10 Solving for variable 'h'. Reorder the terms: -10 + 20h + 160h2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + 20h + 160h2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(-1 + 2h + 16h2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-1 + 2h + 16h2)' equal to zero and attempt to solve: Simplifying -1 + 2h + 16h2 = 0 Solving -1 + 2h + 16h2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.0625 + 0.125h + h2 = 0 Move the constant term to the right: Add '0.0625' to each side of the equation. -0.0625 + 0.125h + 0.0625 + h2 = 0 + 0.0625 Reorder the terms: -0.0625 + 0.0625 + 0.125h + h2 = 0 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + 0.125h + h2 = 0 + 0.0625 0.125h + h2 = 0 + 0.0625 Combine like terms: 0 + 0.0625 = 0.0625 0.125h + h2 = 0.0625 The h term is 0.125h. Take half its coefficient (0.0625). Square it (0.00390625) and add it to both sides. Add '0.00390625' to each side of the equation. 0.125h + 0.00390625 + h2 = 0.0625 + 0.00390625 Reorder the terms: 0.00390625 + 0.125h + h2 = 0.0625 + 0.00390625 Combine like terms: 0.0625 + 0.00390625 = 0.06640625 0.00390625 + 0.125h + h2 = 0.06640625 Factor a perfect square on the left side: (h + 0.0625)(h + 0.0625) = 0.06640625 Calculate the square root of the right side: 0.257694102 Break this problem into two subproblems by setting (h + 0.0625) equal to 0.257694102 and -0.257694102.Subproblem 1
h + 0.0625 = 0.257694102 Simplifying h + 0.0625 = 0.257694102 Reorder the terms: 0.0625 + h = 0.257694102 Solving 0.0625 + h = 0.257694102 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-0.0625' to each side of the equation. 0.0625 + -0.0625 + h = 0.257694102 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + h = 0.257694102 + -0.0625 h = 0.257694102 + -0.0625 Combine like terms: 0.257694102 + -0.0625 = 0.195194102 h = 0.195194102 Simplifying h = 0.195194102Subproblem 2
h + 0.0625 = -0.257694102 Simplifying h + 0.0625 = -0.257694102 Reorder the terms: 0.0625 + h = -0.257694102 Solving 0.0625 + h = -0.257694102 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-0.0625' to each side of the equation. 0.0625 + -0.0625 + h = -0.257694102 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + h = -0.257694102 + -0.0625 h = -0.257694102 + -0.0625 Combine like terms: -0.257694102 + -0.0625 = -0.320194102 h = -0.320194102 Simplifying h = -0.320194102Solution
The solution to the problem is based on the solutions from the subproblems. h = {0.195194102, -0.320194102}Solution
h = {0.195194102, -0.320194102}
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