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Simplifying 64h2 + -28h + -18 = 0 Reorder the terms: -18 + -28h + 64h2 = 0 Solving -18 + -28h + 64h2 = 0 Solving for variable 'h'. Factor out the Greatest Common Factor (GCF), '2'. 2(-9 + -14h + 32h2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-9 + -14h + 32h2)' equal to zero and attempt to solve: Simplifying -9 + -14h + 32h2 = 0 Solving -9 + -14h + 32h2 = 0 Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. -0.28125 + -0.4375h + h2 = 0 Move the constant term to the right: Add '0.28125' to each side of the equation. -0.28125 + -0.4375h + 0.28125 + h2 = 0 + 0.28125 Reorder the terms: -0.28125 + 0.28125 + -0.4375h + h2 = 0 + 0.28125 Combine like terms: -0.28125 + 0.28125 = 0.00000 0.00000 + -0.4375h + h2 = 0 + 0.28125 -0.4375h + h2 = 0 + 0.28125 Combine like terms: 0 + 0.28125 = 0.28125 -0.4375h + h2 = 0.28125 The h term is -0.4375h. Take half its coefficient (-0.21875). Square it (0.0478515625) and add it to both sides. Add '0.0478515625' to each side of the equation. -0.4375h + 0.0478515625 + h2 = 0.28125 + 0.0478515625 Reorder the terms: 0.0478515625 + -0.4375h + h2 = 0.28125 + 0.0478515625 Combine like terms: 0.28125 + 0.0478515625 = 0.3291015625 0.0478515625 + -0.4375h + h2 = 0.3291015625 Factor a perfect square on the left side: (h + -0.21875)(h + -0.21875) = 0.3291015625 Calculate the square root of the right side: 0.573673742 Break this problem into two subproblems by setting (h + -0.21875) equal to 0.573673742 and -0.573673742.Subproblem 1
h + -0.21875 = 0.573673742 Simplifying h + -0.21875 = 0.573673742 Reorder the terms: -0.21875 + h = 0.573673742 Solving -0.21875 + h = 0.573673742 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '0.21875' to each side of the equation. -0.21875 + 0.21875 + h = 0.573673742 + 0.21875 Combine like terms: -0.21875 + 0.21875 = 0.00000 0.00000 + h = 0.573673742 + 0.21875 h = 0.573673742 + 0.21875 Combine like terms: 0.573673742 + 0.21875 = 0.792423742 h = 0.792423742 Simplifying h = 0.792423742Subproblem 2
h + -0.21875 = -0.573673742 Simplifying h + -0.21875 = -0.573673742 Reorder the terms: -0.21875 + h = -0.573673742 Solving -0.21875 + h = -0.573673742 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '0.21875' to each side of the equation. -0.21875 + 0.21875 + h = -0.573673742 + 0.21875 Combine like terms: -0.21875 + 0.21875 = 0.00000 0.00000 + h = -0.573673742 + 0.21875 h = -0.573673742 + 0.21875 Combine like terms: -0.573673742 + 0.21875 = -0.354923742 h = -0.354923742 Simplifying h = -0.354923742Solution
The solution to the problem is based on the solutions from the subproblems. h = {0.792423742, -0.354923742}Solution
h = {0.792423742, -0.354923742}
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