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Simplifying x2 + 4x + -8160 = 0 Reorder the terms: -8160 + 4x + x2 = 0 Solving -8160 + 4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '8160' to each side of the equation. -8160 + 4x + 8160 + x2 = 0 + 8160 Reorder the terms: -8160 + 8160 + 4x + x2 = 0 + 8160 Combine like terms: -8160 + 8160 = 0 0 + 4x + x2 = 0 + 8160 4x + x2 = 0 + 8160 Combine like terms: 0 + 8160 = 8160 4x + x2 = 8160 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 8160 + 4 Reorder the terms: 4 + 4x + x2 = 8160 + 4 Combine like terms: 8160 + 4 = 8164 4 + 4x + x2 = 8164 Factor a perfect square on the left side: (x + 2)(x + 2) = 8164 Calculate the square root of the right side: 90.354855985 Break this problem into two subproblems by setting (x + 2) equal to 90.354855985 and -90.354855985.Subproblem 1
x + 2 = 90.354855985 Simplifying x + 2 = 90.354855985 Reorder the terms: 2 + x = 90.354855985 Solving 2 + x = 90.354855985 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 90.354855985 + -2 Combine like terms: 2 + -2 = 0 0 + x = 90.354855985 + -2 x = 90.354855985 + -2 Combine like terms: 90.354855985 + -2 = 88.354855985 x = 88.354855985 Simplifying x = 88.354855985Subproblem 2
x + 2 = -90.354855985 Simplifying x + 2 = -90.354855985 Reorder the terms: 2 + x = -90.354855985 Solving 2 + x = -90.354855985 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -90.354855985 + -2 Combine like terms: 2 + -2 = 0 0 + x = -90.354855985 + -2 x = -90.354855985 + -2 Combine like terms: -90.354855985 + -2 = -92.354855985 x = -92.354855985 Simplifying x = -92.354855985Solution
The solution to the problem is based on the solutions from the subproblems. x = {88.354855985, -92.354855985}
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