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Simplifying h2 + -5h + -70 = 0 Reorder the terms: -70 + -5h + h2 = 0 Solving -70 + -5h + h2 = 0 Solving for variable 'h'. Begin completing the square. Move the constant term to the right: Add '70' to each side of the equation. -70 + -5h + 70 + h2 = 0 + 70 Reorder the terms: -70 + 70 + -5h + h2 = 0 + 70 Combine like terms: -70 + 70 = 0 0 + -5h + h2 = 0 + 70 -5h + h2 = 0 + 70 Combine like terms: 0 + 70 = 70 -5h + h2 = 70 The h term is -5h. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5h + 6.25 + h2 = 70 + 6.25 Reorder the terms: 6.25 + -5h + h2 = 70 + 6.25 Combine like terms: 70 + 6.25 = 76.25 6.25 + -5h + h2 = 76.25 Factor a perfect square on the left side: (h + -2.5)(h + -2.5) = 76.25 Calculate the square root of the right side: 8.732124598 Break this problem into two subproblems by setting (h + -2.5) equal to 8.732124598 and -8.732124598.Subproblem 1
h + -2.5 = 8.732124598 Simplifying h + -2.5 = 8.732124598 Reorder the terms: -2.5 + h = 8.732124598 Solving -2.5 + h = 8.732124598 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + h = 8.732124598 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + h = 8.732124598 + 2.5 h = 8.732124598 + 2.5 Combine like terms: 8.732124598 + 2.5 = 11.232124598 h = 11.232124598 Simplifying h = 11.232124598Subproblem 2
h + -2.5 = -8.732124598 Simplifying h + -2.5 = -8.732124598 Reorder the terms: -2.5 + h = -8.732124598 Solving -2.5 + h = -8.732124598 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + h = -8.732124598 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + h = -8.732124598 + 2.5 h = -8.732124598 + 2.5 Combine like terms: -8.732124598 + 2.5 = -6.232124598 h = -6.232124598 Simplifying h = -6.232124598Solution
The solution to the problem is based on the solutions from the subproblems. h = {11.232124598, -6.232124598}
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