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Simplifying 13x2 + 44x + 17 = 0 Reorder the terms: 17 + 44x + 13x2 = 0 Solving 17 + 44x + 13x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. 1.307692308 + 3.384615385x + x2 = 0 Move the constant term to the right: Add '-1.307692308' to each side of the equation. 1.307692308 + 3.384615385x + -1.307692308 + x2 = 0 + -1.307692308 Reorder the terms: 1.307692308 + -1.307692308 + 3.384615385x + x2 = 0 + -1.307692308 Combine like terms: 1.307692308 + -1.307692308 = 0.000000000 0.000000000 + 3.384615385x + x2 = 0 + -1.307692308 3.384615385x + x2 = 0 + -1.307692308 Combine like terms: 0 + -1.307692308 = -1.307692308 3.384615385x + x2 = -1.307692308 The x term is 3.384615385x. Take half its coefficient (1.692307693). Square it (2.863905328) and add it to both sides. Add '2.863905328' to each side of the equation. 3.384615385x + 2.863905328 + x2 = -1.307692308 + 2.863905328 Reorder the terms: 2.863905328 + 3.384615385x + x2 = -1.307692308 + 2.863905328 Combine like terms: -1.307692308 + 2.863905328 = 1.55621302 2.863905328 + 3.384615385x + x2 = 1.55621302 Factor a perfect square on the left side: (x + 1.692307693)(x + 1.692307693) = 1.55621302 Calculate the square root of the right side: 1.247482673 Break this problem into two subproblems by setting (x + 1.692307693) equal to 1.247482673 and -1.247482673.Subproblem 1
x + 1.692307693 = 1.247482673 Simplifying x + 1.692307693 = 1.247482673 Reorder the terms: 1.692307693 + x = 1.247482673 Solving 1.692307693 + x = 1.247482673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.692307693' to each side of the equation. 1.692307693 + -1.692307693 + x = 1.247482673 + -1.692307693 Combine like terms: 1.692307693 + -1.692307693 = 0.000000000 0.000000000 + x = 1.247482673 + -1.692307693 x = 1.247482673 + -1.692307693 Combine like terms: 1.247482673 + -1.692307693 = -0.44482502 x = -0.44482502 Simplifying x = -0.44482502Subproblem 2
x + 1.692307693 = -1.247482673 Simplifying x + 1.692307693 = -1.247482673 Reorder the terms: 1.692307693 + x = -1.247482673 Solving 1.692307693 + x = -1.247482673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.692307693' to each side of the equation. 1.692307693 + -1.692307693 + x = -1.247482673 + -1.692307693 Combine like terms: 1.692307693 + -1.692307693 = 0.000000000 0.000000000 + x = -1.247482673 + -1.692307693 x = -1.247482673 + -1.692307693 Combine like terms: -1.247482673 + -1.692307693 = -2.939790366 x = -2.939790366 Simplifying x = -2.939790366Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.44482502, -2.939790366}
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