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Simplifying 1 = 13x2 + 4x Reorder the terms: 1 = 4x + 13x2 Solving 1 = 4x + 13x2 Solving for variable 'x'. Reorder the terms: 1 + -4x + -13x2 = 4x + -4x + 13x2 + -13x2 Combine like terms: 4x + -4x = 0 1 + -4x + -13x2 = 0 + 13x2 + -13x2 1 + -4x + -13x2 = 13x2 + -13x2 Combine like terms: 13x2 + -13x2 = 0 1 + -4x + -13x2 = 0 Begin completing the square. Divide all terms by -13 the coefficient of the squared term: Divide each side by '-13'. -0.07692307692 + 0.3076923077x + x2 = 0 Move the constant term to the right: Add '0.07692307692' to each side of the equation. -0.07692307692 + 0.3076923077x + 0.07692307692 + x2 = 0 + 0.07692307692 Reorder the terms: -0.07692307692 + 0.07692307692 + 0.3076923077x + x2 = 0 + 0.07692307692 Combine like terms: -0.07692307692 + 0.07692307692 = 0.00000000000 0.00000000000 + 0.3076923077x + x2 = 0 + 0.07692307692 0.3076923077x + x2 = 0 + 0.07692307692 Combine like terms: 0 + 0.07692307692 = 0.07692307692 0.3076923077x + x2 = 0.07692307692 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 = 0.07692307692 + 0.02366863907 Reorder the terms: 0.02366863907 + 0.3076923077x + x2 = 0.07692307692 + 0.02366863907 Combine like terms: 0.07692307692 + 0.02366863907 = 0.10059171599 0.02366863907 + 0.3076923077x + x2 = 0.10059171599 Factor a perfect square on the left side: (x + 0.1538461539)(x + 0.1538461539) = 0.10059171599 Calculate the square root of the right side: 0.317161971 Break this problem into two subproblems by setting (x + 0.1538461539) equal to 0.317161971 and -0.317161971.Subproblem 1
x + 0.1538461539 = 0.317161971 Simplifying x + 0.1538461539 = 0.317161971 Reorder the terms: 0.1538461539 + x = 0.317161971 Solving 0.1538461539 + x = 0.317161971 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 = 0.317161971 + -0.1538461539 Combine like terms: 0.1538461539 + -0.1538461539 = 0.0000000000 0.0000000000 + x = 0.317161971 + -0.1538461539 x = 0.317161971 + -0.1538461539 Combine like terms: 0.317161971 + -0.1538461539 = 0.1633158171 x = 0.1633158171 Simplifying x = 0.1633158171Subproblem 2
x + 0.1538461539 = -0.317161971 Simplifying x + 0.1538461539 = -0.317161971 Reorder the terms: 0.1538461539 + x = -0.317161971 Solving 0.1538461539 + x = -0.317161971 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 = -0.317161971 + -0.1538461539 Combine like terms: 0.1538461539 + -0.1538461539 = 0.0000000000 0.0000000000 + x = -0.317161971 + -0.1538461539 x = -0.317161971 + -0.1538461539 Combine like terms: -0.317161971 + -0.1538461539 = -0.4710081249 x = -0.4710081249 Simplifying x = -0.4710081249Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1633158171, -0.4710081249}
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