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Simplifying h * h + 13h + -10 = 0 Multiply h * h h2 + 13h + -10 = 0 Reorder the terms: -10 + 13h + h2 = 0 Solving -10 + 13h + h2 = 0 Solving for variable 'h'. Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + 13h + 10 + h2 = 0 + 10 Reorder the terms: -10 + 10 + 13h + h2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 13h + h2 = 0 + 10 13h + h2 = 0 + 10 Combine like terms: 0 + 10 = 10 13h + h2 = 10 The h term is 13h. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13h + 42.25 + h2 = 10 + 42.25 Reorder the terms: 42.25 + 13h + h2 = 10 + 42.25 Combine like terms: 10 + 42.25 = 52.25 42.25 + 13h + h2 = 52.25 Factor a perfect square on the left side: (h + 6.5)(h + 6.5) = 52.25 Calculate the square root of the right side: 7.228416147 Break this problem into two subproblems by setting (h + 6.5) equal to 7.228416147 and -7.228416147.Subproblem 1
h + 6.5 = 7.228416147 Simplifying h + 6.5 = 7.228416147 Reorder the terms: 6.5 + h = 7.228416147 Solving 6.5 + h = 7.228416147 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + h = 7.228416147 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + h = 7.228416147 + -6.5 h = 7.228416147 + -6.5 Combine like terms: 7.228416147 + -6.5 = 0.728416147 h = 0.728416147 Simplifying h = 0.728416147Subproblem 2
h + 6.5 = -7.228416147 Simplifying h + 6.5 = -7.228416147 Reorder the terms: 6.5 + h = -7.228416147 Solving 6.5 + h = -7.228416147 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + h = -7.228416147 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + h = -7.228416147 + -6.5 h = -7.228416147 + -6.5 Combine like terms: -7.228416147 + -6.5 = -13.728416147 h = -13.728416147 Simplifying h = -13.728416147Solution
The solution to the problem is based on the solutions from the subproblems. h = {0.728416147, -13.728416147}
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