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Simplifying h + -1(h * h) = 0.18 Multiply h * h h + -1(h2) = 0.18 Solving h + -1h2 = 0.18 Solving for variable 'h'. Reorder the terms: -0.18 + h + -1h2 = 0.18 + -0.18 Combine like terms: 0.18 + -0.18 = 0.00 -0.18 + h + -1h2 = 0.00 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 0.18 + -1h + h2 = 0.00 Move the constant term to the right: Add '-0.18' to each side of the equation. 0.18 + -1h + -0.18 + h2 = 0.00 + -0.18 Reorder the terms: 0.18 + -0.18 + -1h + h2 = 0.00 + -0.18 Combine like terms: 0.18 + -0.18 = 0.00 0.00 + -1h + h2 = 0.00 + -0.18 -1h + h2 = 0.00 + -0.18 Combine like terms: 0.00 + -0.18 = -0.18 -1h + h2 = -0.18 The h term is h. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1h + 0.25 + h2 = -0.18 + 0.25 Reorder the terms: 0.25 + -1h + h2 = -0.18 + 0.25 Combine like terms: -0.18 + 0.25 = 0.07 0.25 + -1h + h2 = 0.07 Factor a perfect square on the left side: (h + 0.5)(h + 0.5) = 0.07 Calculate the square root of the right side: 0.264575131 Break this problem into two subproblems by setting (h + 0.5) equal to 0.264575131 and -0.264575131.Subproblem 1
h + 0.5 = 0.264575131 Simplifying h + 0.5 = 0.264575131 Reorder the terms: 0.5 + h = 0.264575131 Solving 0.5 + h = 0.264575131 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + h = 0.264575131 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + h = 0.264575131 + -0.5 h = 0.264575131 + -0.5 Combine like terms: 0.264575131 + -0.5 = -0.235424869 h = -0.235424869 Simplifying h = -0.235424869Subproblem 2
h + 0.5 = -0.264575131 Simplifying h + 0.5 = -0.264575131 Reorder the terms: 0.5 + h = -0.264575131 Solving 0.5 + h = -0.264575131 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + h = -0.264575131 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + h = -0.264575131 + -0.5 h = -0.264575131 + -0.5 Combine like terms: -0.264575131 + -0.5 = -0.764575131 h = -0.764575131 Simplifying h = -0.764575131Solution
The solution to the problem is based on the solutions from the subproblems. h = {-0.235424869, -0.764575131}
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