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Simplifying 5h2 = 3 + -1h Solving 5h2 = 3 + -1h Solving for variable 'h'. Reorder the terms: -3 + h + 5h2 = 3 + -1h + -3 + h Reorder the terms: -3 + h + 5h2 = 3 + -3 + -1h + h Combine like terms: 3 + -3 = 0 -3 + h + 5h2 = 0 + -1h + h -3 + h + 5h2 = -1h + h Combine like terms: -1h + h = 0 -3 + h + 5h2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.6 + 0.2h + h2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + 0.2h + 0.6 + h2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + 0.2h + h2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + 0.2h + h2 = 0 + 0.6 0.2h + h2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 0.2h + h2 = 0.6 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. 0.2h + 0.25 + h2 = 0.6 + 0.25 Reorder the terms: 0.25 + 0.2h + h2 = 0.6 + 0.25 Combine like terms: 0.6 + 0.25 = 0.85 0.25 + 0.2h + h2 = 0.85 Factor a perfect square on the left side: (h + 0.5)(h + 0.5) = 0.85 Calculate the square root of the right side: 0.921954446 Break this problem into two subproblems by setting (h + 0.5) equal to 0.921954446 and -0.921954446.Subproblem 1
h + 0.5 = 0.921954446 Simplifying h + 0.5 = 0.921954446 Reorder the terms: 0.5 + h = 0.921954446 Solving 0.5 + h = 0.921954446 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 = 0.921954446 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + h = 0.921954446 + -0.5 h = 0.921954446 + -0.5 Combine like terms: 0.921954446 + -0.5 = 0.421954446 h = 0.421954446 Simplifying h = 0.421954446Subproblem 2
h + 0.5 = -0.921954446 Simplifying h + 0.5 = -0.921954446 Reorder the terms: 0.5 + h = -0.921954446 Solving 0.5 + h = -0.921954446 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 = -0.921954446 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + h = -0.921954446 + -0.5 h = -0.921954446 + -0.5 Combine like terms: -0.921954446 + -0.5 = -1.421954446 h = -1.421954446 Simplifying h = -1.421954446Solution
The solution to the problem is based on the solutions from the subproblems. h = {0.421954446, -1.421954446}
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