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Simplifying 4x2 + -35x + -414 = 0 Reorder the terms: -414 + -35x + 4x2 = 0 Solving -414 + -35x + 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'. -103.5 + -8.75x + x2 = 0 Move the constant term to the right: Add '103.5' to each side of the equation. -103.5 + -8.75x + 103.5 + x2 = 0 + 103.5 Reorder the terms: -103.5 + 103.5 + -8.75x + x2 = 0 + 103.5 Combine like terms: -103.5 + 103.5 = 0.0 0.0 + -8.75x + x2 = 0 + 103.5 -8.75x + x2 = 0 + 103.5 Combine like terms: 0 + 103.5 = 103.5 -8.75x + x2 = 103.5 The x term is -8.75x. Take half its coefficient (-4.375). Square it (19.140625) and add it to both sides. Add '19.140625' to each side of the equation. -8.75x + 19.140625 + x2 = 103.5 + 19.140625 Reorder the terms: 19.140625 + -8.75x + x2 = 103.5 + 19.140625 Combine like terms: 103.5 + 19.140625 = 122.640625 19.140625 + -8.75x + x2 = 122.640625 Factor a perfect square on the left side: (x + -4.375)(x + -4.375) = 122.640625 Calculate the square root of the right side: 11.074322778 Break this problem into two subproblems by setting (x + -4.375) equal to 11.074322778 and -11.074322778.Subproblem 1
x + -4.375 = 11.074322778 Simplifying x + -4.375 = 11.074322778 Reorder the terms: -4.375 + x = 11.074322778 Solving -4.375 + x = 11.074322778 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.375' to each side of the equation. -4.375 + 4.375 + x = 11.074322778 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + x = 11.074322778 + 4.375 x = 11.074322778 + 4.375 Combine like terms: 11.074322778 + 4.375 = 15.449322778 x = 15.449322778 Simplifying x = 15.449322778Subproblem 2
x + -4.375 = -11.074322778 Simplifying x + -4.375 = -11.074322778 Reorder the terms: -4.375 + x = -11.074322778 Solving -4.375 + x = -11.074322778 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.375' to each side of the equation. -4.375 + 4.375 + x = -11.074322778 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + x = -11.074322778 + 4.375 x = -11.074322778 + 4.375 Combine like terms: -11.074322778 + 4.375 = -6.699322778 x = -6.699322778 Simplifying x = -6.699322778Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.449322778, -6.699322778}
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