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Simplifying 0 = 7h2 + 6h + -1224 Reorder the terms: 0 = -1224 + 6h + 7h2 Solving 0 = -1224 + 6h + 7h2 Solving for variable 'h'. Combine like terms: 0 + 1224 = 1224 1224 + -6h + -7h2 = -1224 + 6h + 7h2 + 1224 + -6h + -7h2 Reorder the terms: 1224 + -6h + -7h2 = -1224 + 1224 + 6h + -6h + 7h2 + -7h2 Combine like terms: -1224 + 1224 = 0 1224 + -6h + -7h2 = 0 + 6h + -6h + 7h2 + -7h2 1224 + -6h + -7h2 = 6h + -6h + 7h2 + -7h2 Combine like terms: 6h + -6h = 0 1224 + -6h + -7h2 = 0 + 7h2 + -7h2 1224 + -6h + -7h2 = 7h2 + -7h2 Combine like terms: 7h2 + -7h2 = 0 1224 + -6h + -7h2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -174.8571429 + 0.8571428571h + h2 = 0 Move the constant term to the right: Add '174.8571429' to each side of the equation. -174.8571429 + 0.8571428571h + 174.8571429 + h2 = 0 + 174.8571429 Reorder the terms: -174.8571429 + 174.8571429 + 0.8571428571h + h2 = 0 + 174.8571429 Combine like terms: -174.8571429 + 174.8571429 = 0.0000000 0.0000000 + 0.8571428571h + h2 = 0 + 174.8571429 0.8571428571h + h2 = 0 + 174.8571429 Combine like terms: 0 + 174.8571429 = 174.8571429 0.8571428571h + h2 = 174.8571429 The h term is 0.8571428571h. Take half its coefficient (0.4285714286). Square it (0.1836734694) and add it to both sides. Add '0.1836734694' to each side of the equation. 0.8571428571h + 0.1836734694 + h2 = 174.8571429 + 0.1836734694 Reorder the terms: 0.1836734694 + 0.8571428571h + h2 = 174.8571429 + 0.1836734694 Combine like terms: 174.8571429 + 0.1836734694 = 175.0408163694 0.1836734694 + 0.8571428571h + h2 = 175.0408163694 Factor a perfect square on the left side: (h + 0.4285714286)(h + 0.4285714286) = 175.0408163694 Calculate the square root of the right side: 13.230299179 Break this problem into two subproblems by setting (h + 0.4285714286) equal to 13.230299179 and -13.230299179.Subproblem 1
h + 0.4285714286 = 13.230299179 Simplifying h + 0.4285714286 = 13.230299179 Reorder the terms: 0.4285714286 + h = 13.230299179 Solving 0.4285714286 + h = 13.230299179 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-0.4285714286' to each side of the equation. 0.4285714286 + -0.4285714286 + h = 13.230299179 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + h = 13.230299179 + -0.4285714286 h = 13.230299179 + -0.4285714286 Combine like terms: 13.230299179 + -0.4285714286 = 12.8017277504 h = 12.8017277504 Simplifying h = 12.8017277504Subproblem 2
h + 0.4285714286 = -13.230299179 Simplifying h + 0.4285714286 = -13.230299179 Reorder the terms: 0.4285714286 + h = -13.230299179 Solving 0.4285714286 + h = -13.230299179 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-0.4285714286' to each side of the equation. 0.4285714286 + -0.4285714286 + h = -13.230299179 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + h = -13.230299179 + -0.4285714286 h = -13.230299179 + -0.4285714286 Combine like terms: -13.230299179 + -0.4285714286 = -13.6588706076 h = -13.6588706076 Simplifying h = -13.6588706076Solution
The solution to the problem is based on the solutions from the subproblems. h = {12.8017277504, -13.6588706076}
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