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Simplifying 7h(90 + -1h) = 210 (90 * 7h + -1h * 7h) = 210 (630h + -7h2) = 210 Solving 630h + -7h2 = 210 Solving for variable 'h'. Reorder the terms: -210 + 630h + -7h2 = 210 + -210 Combine like terms: 210 + -210 = 0 -210 + 630h + -7h2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(-30 + 90h + -1h2) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(-30 + 90h + -1h2)' equal to zero and attempt to solve: Simplifying -30 + 90h + -1h2 = 0 Solving -30 + 90h + -1h2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 30 + -90h + h2 = 0 Move the constant term to the right: Add '-30' to each side of the equation. 30 + -90h + -30 + h2 = 0 + -30 Reorder the terms: 30 + -30 + -90h + h2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -90h + h2 = 0 + -30 -90h + h2 = 0 + -30 Combine like terms: 0 + -30 = -30 -90h + h2 = -30 The h term is -90h. Take half its coefficient (-45). Square it (2025) and add it to both sides. Add '2025' to each side of the equation. -90h + 2025 + h2 = -30 + 2025 Reorder the terms: 2025 + -90h + h2 = -30 + 2025 Combine like terms: -30 + 2025 = 1995 2025 + -90h + h2 = 1995 Factor a perfect square on the left side: (h + -45)(h + -45) = 1995 Calculate the square root of the right side: 44.665422868 Break this problem into two subproblems by setting (h + -45) equal to 44.665422868 and -44.665422868.Subproblem 1
h + -45 = 44.665422868 Simplifying h + -45 = 44.665422868 Reorder the terms: -45 + h = 44.665422868 Solving -45 + h = 44.665422868 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '45' to each side of the equation. -45 + 45 + h = 44.665422868 + 45 Combine like terms: -45 + 45 = 0 0 + h = 44.665422868 + 45 h = 44.665422868 + 45 Combine like terms: 44.665422868 + 45 = 89.665422868 h = 89.665422868 Simplifying h = 89.665422868Subproblem 2
h + -45 = -44.665422868 Simplifying h + -45 = -44.665422868 Reorder the terms: -45 + h = -44.665422868 Solving -45 + h = -44.665422868 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '45' to each side of the equation. -45 + 45 + h = -44.665422868 + 45 Combine like terms: -45 + 45 = 0 0 + h = -44.665422868 + 45 h = -44.665422868 + 45 Combine like terms: -44.665422868 + 45 = 0.334577132 h = 0.334577132 Simplifying h = 0.334577132Solution
The solution to the problem is based on the solutions from the subproblems. h = {89.665422868, 0.334577132}Solution
h = {89.665422868, 0.334577132}
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