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Simplifying 4x + 59 = 13x2 + 17 Reorder the terms: 59 + 4x = 13x2 + 17 Reorder the terms: 59 + 4x = 17 + 13x2 Solving 59 + 4x = 17 + 13x2 Solving for variable 'x'. Reorder the terms: 59 + -17 + 4x + -13x2 = 17 + 13x2 + -17 + -13x2 Combine like terms: 59 + -17 = 42 42 + 4x + -13x2 = 17 + 13x2 + -17 + -13x2 Reorder the terms: 42 + 4x + -13x2 = 17 + -17 + 13x2 + -13x2 Combine like terms: 17 + -17 = 0 42 + 4x + -13x2 = 0 + 13x2 + -13x2 42 + 4x + -13x2 = 13x2 + -13x2 Combine like terms: 13x2 + -13x2 = 0 42 + 4x + -13x2 = 0 Begin completing the square. Divide all terms by -13 the coefficient of the squared term: Divide each side by '-13'. -3.230769231 + -0.3076923077x + x2 = 0 Move the constant term to the right: Add '3.230769231' to each side of the equation. -3.230769231 + -0.3076923077x + 3.230769231 + x2 = 0 + 3.230769231 Reorder the terms: -3.230769231 + 3.230769231 + -0.3076923077x + x2 = 0 + 3.230769231 Combine like terms: -3.230769231 + 3.230769231 = 0.000000000 0.000000000 + -0.3076923077x + x2 = 0 + 3.230769231 -0.3076923077x + x2 = 0 + 3.230769231 Combine like terms: 0 + 3.230769231 = 3.230769231 -0.3076923077x + x2 = 3.230769231 The x term is -0.3076923077x. Take half its coefficient (-0.1538461539). Square it (0.02366863907) and add it to both sides. Add '0.02366863907' to each side of the equation. -0.3076923077x + 0.02366863907 + x2 = 3.230769231 + 0.02366863907 Reorder the terms: 0.02366863907 + -0.3076923077x + x2 = 3.230769231 + 0.02366863907 Combine like terms: 3.230769231 + 0.02366863907 = 3.25443787007 0.02366863907 + -0.3076923077x + x2 = 3.25443787007 Factor a perfect square on the left side: (x + -0.1538461539)(x + -0.1538461539) = 3.25443787007 Calculate the square root of the right side: 1.804006062 Break this problem into two subproblems by setting (x + -0.1538461539) equal to 1.804006062 and -1.804006062.Subproblem 1
x + -0.1538461539 = 1.804006062 Simplifying x + -0.1538461539 = 1.804006062 Reorder the terms: -0.1538461539 + x = 1.804006062 Solving -0.1538461539 + x = 1.804006062 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1538461539' to each side of the equation. -0.1538461539 + 0.1538461539 + x = 1.804006062 + 0.1538461539 Combine like terms: -0.1538461539 + 0.1538461539 = 0.0000000000 0.0000000000 + x = 1.804006062 + 0.1538461539 x = 1.804006062 + 0.1538461539 Combine like terms: 1.804006062 + 0.1538461539 = 1.9578522159 x = 1.9578522159 Simplifying x = 1.9578522159Subproblem 2
x + -0.1538461539 = -1.804006062 Simplifying x + -0.1538461539 = -1.804006062 Reorder the terms: -0.1538461539 + x = -1.804006062 Solving -0.1538461539 + x = -1.804006062 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1538461539' to each side of the equation. -0.1538461539 + 0.1538461539 + x = -1.804006062 + 0.1538461539 Combine like terms: -0.1538461539 + 0.1538461539 = 0.0000000000 0.0000000000 + x = -1.804006062 + 0.1538461539 x = -1.804006062 + 0.1538461539 Combine like terms: -1.804006062 + 0.1538461539 = -1.6501599081 x = -1.6501599081 Simplifying x = -1.6501599081Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.9578522159, -1.6501599081}
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