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Simplifying 4x2 + 83x + 360 = 0 Reorder the terms: 360 + 83x + 4x2 = 0 Solving 360 + 83x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 90 + 20.75x + x2 = 0 Move the constant term to the right: Add '-90' to each side of the equation. 90 + 20.75x + -90 + x2 = 0 + -90 Reorder the terms: 90 + -90 + 20.75x + x2 = 0 + -90 Combine like terms: 90 + -90 = 0 0 + 20.75x + x2 = 0 + -90 20.75x + x2 = 0 + -90 Combine like terms: 0 + -90 = -90 20.75x + x2 = -90 The x term is 20.75x. Take half its coefficient (10.375). Square it (107.640625) and add it to both sides. Add '107.640625' to each side of the equation. 20.75x + 107.640625 + x2 = -90 + 107.640625 Reorder the terms: 107.640625 + 20.75x + x2 = -90 + 107.640625 Combine like terms: -90 + 107.640625 = 17.640625 107.640625 + 20.75x + x2 = 17.640625 Factor a perfect square on the left side: (x + 10.375)(x + 10.375) = 17.640625 Calculate the square root of the right side: 4.200074404 Break this problem into two subproblems by setting (x + 10.375) equal to 4.200074404 and -4.200074404.Subproblem 1
x + 10.375 = 4.200074404 Simplifying x + 10.375 = 4.200074404 Reorder the terms: 10.375 + x = 4.200074404 Solving 10.375 + x = 4.200074404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.375' to each side of the equation. 10.375 + -10.375 + x = 4.200074404 + -10.375 Combine like terms: 10.375 + -10.375 = 0.000 0.000 + x = 4.200074404 + -10.375 x = 4.200074404 + -10.375 Combine like terms: 4.200074404 + -10.375 = -6.174925596 x = -6.174925596 Simplifying x = -6.174925596Subproblem 2
x + 10.375 = -4.200074404 Simplifying x + 10.375 = -4.200074404 Reorder the terms: 10.375 + x = -4.200074404 Solving 10.375 + x = -4.200074404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.375' to each side of the equation. 10.375 + -10.375 + x = -4.200074404 + -10.375 Combine like terms: 10.375 + -10.375 = 0.000 0.000 + x = -4.200074404 + -10.375 x = -4.200074404 + -10.375 Combine like terms: -4.200074404 + -10.375 = -14.575074404 x = -14.575074404 Simplifying x = -14.575074404Solution
The solution to the problem is based on the solutions from the subproblems. x = {-6.174925596, -14.575074404}
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