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Simplifying 15 = h2 + 4h Reorder the terms: 15 = 4h + h2 Solving 15 = 4h + h2 Solving for variable 'h'. Reorder the terms: 15 + -4h + -1h2 = 4h + -4h + h2 + -1h2 Combine like terms: 4h + -4h = 0 15 + -4h + -1h2 = 0 + h2 + -1h2 15 + -4h + -1h2 = h2 + -1h2 Combine like terms: h2 + -1h2 = 0 15 + -4h + -1h2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -15 + 4h + h2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + 4h + 15 + h2 = 0 + 15 Reorder the terms: -15 + 15 + 4h + h2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 4h + h2 = 0 + 15 4h + h2 = 0 + 15 Combine like terms: 0 + 15 = 15 4h + h2 = 15 The h term is 4h. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4h + 4 + h2 = 15 + 4 Reorder the terms: 4 + 4h + h2 = 15 + 4 Combine like terms: 15 + 4 = 19 4 + 4h + h2 = 19 Factor a perfect square on the left side: (h + 2)(h + 2) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (h + 2) equal to 4.358898944 and -4.358898944.Subproblem 1
h + 2 = 4.358898944 Simplifying h + 2 = 4.358898944 Reorder the terms: 2 + h = 4.358898944 Solving 2 + h = 4.358898944 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + h = 4.358898944 + -2 Combine like terms: 2 + -2 = 0 0 + h = 4.358898944 + -2 h = 4.358898944 + -2 Combine like terms: 4.358898944 + -2 = 2.358898944 h = 2.358898944 Simplifying h = 2.358898944Subproblem 2
h + 2 = -4.358898944 Simplifying h + 2 = -4.358898944 Reorder the terms: 2 + h = -4.358898944 Solving 2 + h = -4.358898944 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + h = -4.358898944 + -2 Combine like terms: 2 + -2 = 0 0 + h = -4.358898944 + -2 h = -4.358898944 + -2 Combine like terms: -4.358898944 + -2 = -6.358898944 h = -6.358898944 Simplifying h = -6.358898944Solution
The solution to the problem is based on the solutions from the subproblems. h = {2.358898944, -6.358898944}
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