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Simplifying 19 = -4h(h + 5) + h Reorder the terms: 19 = -4h(5 + h) + h 19 = (5 * -4h + h * -4h) + h 19 = (-20h + -4h2) + h Reorder the terms: 19 = -20h + h + -4h2 Combine like terms: -20h + h = -19h 19 = -19h + -4h2 Solving 19 = -19h + -4h2 Solving for variable 'h'. Reorder the terms: 19 + 19h + 4h2 = -19h + 19h + -4h2 + 4h2 Combine like terms: -19h + 19h = 0 19 + 19h + 4h2 = 0 + -4h2 + 4h2 19 + 19h + 4h2 = -4h2 + 4h2 Combine like terms: -4h2 + 4h2 = 0 19 + 19h + 4h2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 4.75 + 4.75h + h2 = 0 Move the constant term to the right: Add '-4.75' to each side of the equation. 4.75 + 4.75h + -4.75 + h2 = 0 + -4.75 Reorder the terms: 4.75 + -4.75 + 4.75h + h2 = 0 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + 4.75h + h2 = 0 + -4.75 4.75h + h2 = 0 + -4.75 Combine like terms: 0 + -4.75 = -4.75 4.75h + h2 = -4.75 The h term is 4.75h. Take half its coefficient (2.375). Square it (5.640625) and add it to both sides. Add '5.640625' to each side of the equation. 4.75h + 5.640625 + h2 = -4.75 + 5.640625 Reorder the terms: 5.640625 + 4.75h + h2 = -4.75 + 5.640625 Combine like terms: -4.75 + 5.640625 = 0.890625 5.640625 + 4.75h + h2 = 0.890625 Factor a perfect square on the left side: (h + 2.375)(h + 2.375) = 0.890625 Calculate the square root of the right side: 0.943729304 Break this problem into two subproblems by setting (h + 2.375) equal to 0.943729304 and -0.943729304.Subproblem 1
h + 2.375 = 0.943729304 Simplifying h + 2.375 = 0.943729304 Reorder the terms: 2.375 + h = 0.943729304 Solving 2.375 + h = 0.943729304 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-2.375' to each side of the equation. 2.375 + -2.375 + h = 0.943729304 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + h = 0.943729304 + -2.375 h = 0.943729304 + -2.375 Combine like terms: 0.943729304 + -2.375 = -1.431270696 h = -1.431270696 Simplifying h = -1.431270696Subproblem 2
h + 2.375 = -0.943729304 Simplifying h + 2.375 = -0.943729304 Reorder the terms: 2.375 + h = -0.943729304 Solving 2.375 + h = -0.943729304 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-2.375' to each side of the equation. 2.375 + -2.375 + h = -0.943729304 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + h = -0.943729304 + -2.375 h = -0.943729304 + -2.375 Combine like terms: -0.943729304 + -2.375 = -3.318729304 h = -3.318729304 Simplifying h = -3.318729304Solution
The solution to the problem is based on the solutions from the subproblems. h = {-1.431270696, -3.318729304}
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