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Simplifying h(2h + -3) = 35(35) Reorder the terms: h(-3 + 2h) = 35(35) (-3 * h + 2h * h) = 35(35) (-3h + 2h2) = 35(35) Multiply 35 * 35 -3h + 2h2 = 1225 Solving -3h + 2h2 = 1225 Solving for variable 'h'. Reorder the terms: -1225 + -3h + 2h2 = 1225 + -1225 Combine like terms: 1225 + -1225 = 0 -1225 + -3h + 2h2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -612.5 + -1.5h + h2 = 0 Move the constant term to the right: Add '612.5' to each side of the equation. -612.5 + -1.5h + 612.5 + h2 = 0 + 612.5 Reorder the terms: -612.5 + 612.5 + -1.5h + h2 = 0 + 612.5 Combine like terms: -612.5 + 612.5 = 0.0 0.0 + -1.5h + h2 = 0 + 612.5 -1.5h + h2 = 0 + 612.5 Combine like terms: 0 + 612.5 = 612.5 -1.5h + h2 = 612.5 The h term is -1.5h. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5h + 0.5625 + h2 = 612.5 + 0.5625 Reorder the terms: 0.5625 + -1.5h + h2 = 612.5 + 0.5625 Combine like terms: 612.5 + 0.5625 = 613.0625 0.5625 + -1.5h + h2 = 613.0625 Factor a perfect square on the left side: (h + -0.75)(h + -0.75) = 613.0625 Calculate the square root of the right side: 24.76009895 Break this problem into two subproblems by setting (h + -0.75) equal to 24.76009895 and -24.76009895.Subproblem 1
h + -0.75 = 24.76009895 Simplifying h + -0.75 = 24.76009895 Reorder the terms: -0.75 + h = 24.76009895 Solving -0.75 + h = 24.76009895 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + h = 24.76009895 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + h = 24.76009895 + 0.75 h = 24.76009895 + 0.75 Combine like terms: 24.76009895 + 0.75 = 25.51009895 h = 25.51009895 Simplifying h = 25.51009895Subproblem 2
h + -0.75 = -24.76009895 Simplifying h + -0.75 = -24.76009895 Reorder the terms: -0.75 + h = -24.76009895 Solving -0.75 + h = -24.76009895 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + h = -24.76009895 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + h = -24.76009895 + 0.75 h = -24.76009895 + 0.75 Combine like terms: -24.76009895 + 0.75 = -24.01009895 h = -24.01009895 Simplifying h = -24.01009895Solution
The solution to the problem is based on the solutions from the subproblems. h = {25.51009895, -24.01009895}
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