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Simplifying 4x + 1 + -4 = x2 + 21x + -14 Reorder the terms: 1 + -4 + 4x = x2 + 21x + -14 Combine like terms: 1 + -4 = -3 -3 + 4x = x2 + 21x + -14 Reorder the terms: -3 + 4x = -14 + 21x + x2 Solving -3 + 4x = -14 + 21x + x2 Solving for variable 'x'. Reorder the terms: -3 + 14 + 4x + -21x + -1x2 = -14 + 21x + x2 + 14 + -21x + -1x2 Combine like terms: -3 + 14 = 11 11 + 4x + -21x + -1x2 = -14 + 21x + x2 + 14 + -21x + -1x2 Combine like terms: 4x + -21x = -17x 11 + -17x + -1x2 = -14 + 21x + x2 + 14 + -21x + -1x2 Reorder the terms: 11 + -17x + -1x2 = -14 + 14 + 21x + -21x + x2 + -1x2 Combine like terms: -14 + 14 = 0 11 + -17x + -1x2 = 0 + 21x + -21x + x2 + -1x2 11 + -17x + -1x2 = 21x + -21x + x2 + -1x2 Combine like terms: 21x + -21x = 0 11 + -17x + -1x2 = 0 + x2 + -1x2 11 + -17x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 11 + -17x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -11 + 17x + x2 = 0 Move the constant term to the right: Add '11' to each side of the equation. -11 + 17x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + 17x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 17x + x2 = 0 + 11 17x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 17x + x2 = 11 The x term is 17x. Take half its coefficient (8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. 17x + 72.25 + x2 = 11 + 72.25 Reorder the terms: 72.25 + 17x + x2 = 11 + 72.25 Combine like terms: 11 + 72.25 = 83.25 72.25 + 17x + x2 = 83.25 Factor a perfect square on the left side: (x + 8.5)(x + 8.5) = 83.25 Calculate the square root of the right side: 9.124143795 Break this problem into two subproblems by setting (x + 8.5) equal to 9.124143795 and -9.124143795.Subproblem 1
x + 8.5 = 9.124143795 Simplifying x + 8.5 = 9.124143795 Reorder the terms: 8.5 + x = 9.124143795 Solving 8.5 + x = 9.124143795 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = 9.124143795 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = 9.124143795 + -8.5 x = 9.124143795 + -8.5 Combine like terms: 9.124143795 + -8.5 = 0.624143795 x = 0.624143795 Simplifying x = 0.624143795Subproblem 2
x + 8.5 = -9.124143795 Simplifying x + 8.5 = -9.124143795 Reorder the terms: 8.5 + x = -9.124143795 Solving 8.5 + x = -9.124143795 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = -9.124143795 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = -9.124143795 + -8.5 x = -9.124143795 + -8.5 Combine like terms: -9.124143795 + -8.5 = -17.624143795 x = -17.624143795 Simplifying x = -17.624143795Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.624143795, -17.624143795}
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