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Simplifying 4x2 + -11x + -63 = 0 Reorder the terms: -63 + -11x + 4x2 = 0 Solving -63 + -11x + 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'. -15.75 + -2.75x + x2 = 0 Move the constant term to the right: Add '15.75' to each side of the equation. -15.75 + -2.75x + 15.75 + x2 = 0 + 15.75 Reorder the terms: -15.75 + 15.75 + -2.75x + x2 = 0 + 15.75 Combine like terms: -15.75 + 15.75 = 0.00 0.00 + -2.75x + x2 = 0 + 15.75 -2.75x + x2 = 0 + 15.75 Combine like terms: 0 + 15.75 = 15.75 -2.75x + x2 = 15.75 The x term is -2.75x. Take half its coefficient (-1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. -2.75x + 1.890625 + x2 = 15.75 + 1.890625 Reorder the terms: 1.890625 + -2.75x + x2 = 15.75 + 1.890625 Combine like terms: 15.75 + 1.890625 = 17.640625 1.890625 + -2.75x + x2 = 17.640625 Factor a perfect square on the left side: (x + -1.375)(x + -1.375) = 17.640625 Calculate the square root of the right side: 4.200074404 Break this problem into two subproblems by setting (x + -1.375) equal to 4.200074404 and -4.200074404.Subproblem 1
x + -1.375 = 4.200074404 Simplifying x + -1.375 = 4.200074404 Reorder the terms: -1.375 + x = 4.200074404 Solving -1.375 + x = 4.200074404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + x = 4.200074404 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = 4.200074404 + 1.375 x = 4.200074404 + 1.375 Combine like terms: 4.200074404 + 1.375 = 5.575074404 x = 5.575074404 Simplifying x = 5.575074404Subproblem 2
x + -1.375 = -4.200074404 Simplifying x + -1.375 = -4.200074404 Reorder the terms: -1.375 + x = -4.200074404 Solving -1.375 + x = -4.200074404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + x = -4.200074404 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = -4.200074404 + 1.375 x = -4.200074404 + 1.375 Combine like terms: -4.200074404 + 1.375 = -2.825074404 x = -2.825074404 Simplifying x = -2.825074404Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.575074404, -2.825074404}
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