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Simplifying 471.23 = 6.28h2 + 6.28h + 2h Reorder the terms: 471.23 = 6.28h + 2h + 6.28h2 Combine like terms: 6.28h + 2h = 8.28h 471.23 = 8.28h + 6.28h2 Solving 471.23 = 8.28h + 6.28h2 Solving for variable 'h'. Reorder the terms: 471.23 + -8.28h + -6.28h2 = 8.28h + -8.28h + 6.28h2 + -6.28h2 Combine like terms: 8.28h + -8.28h = 0.00 471.23 + -8.28h + -6.28h2 = 0.00 + 6.28h2 + -6.28h2 471.23 + -8.28h + -6.28h2 = 6.28h2 + -6.28h2 Combine like terms: 6.28h2 + -6.28h2 = 0.00 471.23 + -8.28h + -6.28h2 = 0.00 Begin completing the square. Divide all terms by -6.28 the coefficient of the squared term: Divide each side by '-6.28'. -75.0366242 + 1.318471338h + h2 = 0 Move the constant term to the right: Add '75.0366242' to each side of the equation. -75.0366242 + 1.318471338h + 75.0366242 + h2 = 0 + 75.0366242 Reorder the terms: -75.0366242 + 75.0366242 + 1.318471338h + h2 = 0 + 75.0366242 Combine like terms: -75.0366242 + 75.0366242 = 0.0000000 0.0000000 + 1.318471338h + h2 = 0 + 75.0366242 1.318471338h + h2 = 0 + 75.0366242 Combine like terms: 0 + 75.0366242 = 75.0366242 1.318471338h + h2 = 75.0366242 The h term is 1.318471338h. Take half its coefficient (0.659235669). Square it (0.4345916673) and add it to both sides. Add '0.4345916673' to each side of the equation. 1.318471338h + 0.4345916673 + h2 = 75.0366242 + 0.4345916673 Reorder the terms: 0.4345916673 + 1.318471338h + h2 = 75.0366242 + 0.4345916673 Combine like terms: 75.0366242 + 0.4345916673 = 75.4712158673 0.4345916673 + 1.318471338h + h2 = 75.4712158673 Factor a perfect square on the left side: (h + 0.659235669)(h + 0.659235669) = 75.4712158673 Calculate the square root of the right side: 8.6874171 Break this problem into two subproblems by setting (h + 0.659235669) equal to 8.6874171 and -8.6874171.Subproblem 1
h + 0.659235669 = 8.6874171 Simplifying h + 0.659235669 = 8.6874171 Reorder the terms: 0.659235669 + h = 8.6874171 Solving 0.659235669 + h = 8.6874171 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-0.659235669' to each side of the equation. 0.659235669 + -0.659235669 + h = 8.6874171 + -0.659235669 Combine like terms: 0.659235669 + -0.659235669 = 0.000000000 0.000000000 + h = 8.6874171 + -0.659235669 h = 8.6874171 + -0.659235669 Combine like terms: 8.6874171 + -0.659235669 = 8.028181431 h = 8.028181431 Simplifying h = 8.028181431Subproblem 2
h + 0.659235669 = -8.6874171 Simplifying h + 0.659235669 = -8.6874171 Reorder the terms: 0.659235669 + h = -8.6874171 Solving 0.659235669 + h = -8.6874171 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-0.659235669' to each side of the equation. 0.659235669 + -0.659235669 + h = -8.6874171 + -0.659235669 Combine like terms: 0.659235669 + -0.659235669 = 0.000000000 0.000000000 + h = -8.6874171 + -0.659235669 h = -8.6874171 + -0.659235669 Combine like terms: -8.6874171 + -0.659235669 = -9.346652769 h = -9.346652769 Simplifying h = -9.346652769Solution
The solution to the problem is based on the solutions from the subproblems. h = {8.028181431, -9.346652769}
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