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Simplifying h4 + -1010h2 = -9 Reorder the terms: -1010h2 + h4 = -9 Solving -1010h2 + h4 = -9 Solving for variable 'h'. Reorder the terms: 9 + -1010h2 + h4 = -9 + 9 Combine like terms: -9 + 9 = 0 9 + -1010h2 + h4 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + -1010h2 + -9 + h4 = 0 + -9 Reorder the terms: 9 + -9 + -1010h2 + h4 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1010h2 + h4 = 0 + -9 -1010h2 + h4 = 0 + -9 Combine like terms: 0 + -9 = -9 -1010h2 + h4 = -9 The h term is -1010h2. Take half its coefficient (-505). Square it (255025) and add it to both sides. Add '255025' to each side of the equation. -1010h2 + 255025 + h4 = -9 + 255025 Reorder the terms: 255025 + -1010h2 + h4 = -9 + 255025 Combine like terms: -9 + 255025 = 255016 255025 + -1010h2 + h4 = 255016 Factor a perfect square on the left side: (h2 + -505)(h2 + -505) = 255016 Calculate the square root of the right side: 504.99108903 Break this problem into two subproblems by setting (h2 + -505) equal to 504.99108903 and -504.99108903.Subproblem 1
h2 + -505 = 504.99108903 Simplifying h2 + -505 = 504.99108903 Reorder the terms: -505 + h2 = 504.99108903 Solving -505 + h2 = 504.99108903 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '505' to each side of the equation. -505 + 505 + h2 = 504.99108903 + 505 Combine like terms: -505 + 505 = 0 0 + h2 = 504.99108903 + 505 h2 = 504.99108903 + 505 Combine like terms: 504.99108903 + 505 = 1009.99108903 h2 = 1009.99108903 Simplifying h2 = 1009.99108903 Take the square root of each side: h = {-31.780356968, 31.780356968}Subproblem 2
h2 + -505 = -504.99108903 Simplifying h2 + -505 = -504.99108903 Reorder the terms: -505 + h2 = -504.99108903 Solving -505 + h2 = -504.99108903 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '505' to each side of the equation. -505 + 505 + h2 = -504.99108903 + 505 Combine like terms: -505 + 505 = 0 0 + h2 = -504.99108903 + 505 h2 = -504.99108903 + 505 Combine like terms: -504.99108903 + 505 = 0.00891097 h2 = 0.00891097 Simplifying h2 = 0.00891097 Take the square root of each side: h = {-0.094397934, 0.094397934}Solution
The solution to the problem is based on the solutions from the subproblems. h = {-31.780356968, 31.780356968, -0.094397934, 0.094397934}
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