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Simplifying 2.4h + 1 = 7h(2h + -4) Reorder the terms: 1 + 2.4h = 7h(2h + -4) Reorder the terms: 1 + 2.4h = 7h(-4 + 2h) 1 + 2.4h = (-4 * 7h + 2h * 7h) 1 + 2.4h = (-28h + 14h2) Solving 1 + 2.4h = -28h + 14h2 Solving for variable 'h'. Combine like terms: 2.4h + 28h = 30.4h 1 + 30.4h + -14h2 = -28h + 14h2 + 28h + -14h2 Reorder the terms: 1 + 30.4h + -14h2 = -28h + 28h + 14h2 + -14h2 Combine like terms: -28h + 28h = 0 1 + 30.4h + -14h2 = 0 + 14h2 + -14h2 1 + 30.4h + -14h2 = 14h2 + -14h2 Combine like terms: 14h2 + -14h2 = 0 1 + 30.4h + -14h2 = 0 Begin completing the square. Divide all terms by -14 the coefficient of the squared term: Divide each side by '-14'. -0.07142857143 + -2.171428571h + h2 = 0 Move the constant term to the right: Add '0.07142857143' to each side of the equation. -0.07142857143 + -2.171428571h + 0.07142857143 + h2 = 0 + 0.07142857143 Reorder the terms: -0.07142857143 + 0.07142857143 + -2.171428571h + h2 = 0 + 0.07142857143 Combine like terms: -0.07142857143 + 0.07142857143 = 0.00000000000 0.00000000000 + -2.171428571h + h2 = 0 + 0.07142857143 -2.171428571h + h2 = 0 + 0.07142857143 Combine like terms: 0 + 0.07142857143 = 0.07142857143 -2.171428571h + h2 = 0.07142857143 The h term is -2.171428571h. Take half its coefficient (-1.085714286). Square it (1.178775511) and add it to both sides. Add '1.178775511' to each side of the equation. -2.171428571h + 1.178775511 + h2 = 0.07142857143 + 1.178775511 Reorder the terms: 1.178775511 + -2.171428571h + h2 = 0.07142857143 + 1.178775511 Combine like terms: 0.07142857143 + 1.178775511 = 1.25020408243 1.178775511 + -2.171428571h + h2 = 1.25020408243 Factor a perfect square on the left side: (h + -1.085714286)(h + -1.085714286) = 1.25020408243 Calculate the square root of the right side: 1.118125253 Break this problem into two subproblems by setting (h + -1.085714286) equal to 1.118125253 and -1.118125253.Subproblem 1
h + -1.085714286 = 1.118125253 Simplifying h + -1.085714286 = 1.118125253 Reorder the terms: -1.085714286 + h = 1.118125253 Solving -1.085714286 + h = 1.118125253 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '1.085714286' to each side of the equation. -1.085714286 + 1.085714286 + h = 1.118125253 + 1.085714286 Combine like terms: -1.085714286 + 1.085714286 = 0.000000000 0.000000000 + h = 1.118125253 + 1.085714286 h = 1.118125253 + 1.085714286 Combine like terms: 1.118125253 + 1.085714286 = 2.203839539 h = 2.203839539 Simplifying h = 2.203839539Subproblem 2
h + -1.085714286 = -1.118125253 Simplifying h + -1.085714286 = -1.118125253 Reorder the terms: -1.085714286 + h = -1.118125253 Solving -1.085714286 + h = -1.118125253 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '1.085714286' to each side of the equation. -1.085714286 + 1.085714286 + h = -1.118125253 + 1.085714286 Combine like terms: -1.085714286 + 1.085714286 = 0.000000000 0.000000000 + h = -1.118125253 + 1.085714286 h = -1.118125253 + 1.085714286 Combine like terms: -1.118125253 + 1.085714286 = -0.032410967 h = -0.032410967 Simplifying h = -0.032410967Solution
The solution to the problem is based on the solutions from the subproblems. h = {2.203839539, -0.032410967}
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