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Simplifying 4x = 13x2 + -5 Reorder the terms: 4x = -5 + 13x2 Solving 4x = -5 + 13x2 Solving for variable 'x'. Reorder the terms: 5 + 4x + -13x2 = -5 + 13x2 + 5 + -13x2 Reorder the terms: 5 + 4x + -13x2 = -5 + 5 + 13x2 + -13x2 Combine like terms: -5 + 5 = 0 5 + 4x + -13x2 = 0 + 13x2 + -13x2 5 + 4x + -13x2 = 13x2 + -13x2 Combine like terms: 13x2 + -13x2 = 0 5 + 4x + -13x2 = 0 Begin completing the square. Divide all terms by -13 the coefficient of the squared term: Divide each side by '-13'. -0.3846153846 + -0.3076923077x + x2 = 0 Move the constant term to the right: Add '0.3846153846' to each side of the equation. -0.3846153846 + -0.3076923077x + 0.3846153846 + x2 = 0 + 0.3846153846 Reorder the terms: -0.3846153846 + 0.3846153846 + -0.3076923077x + x2 = 0 + 0.3846153846 Combine like terms: -0.3846153846 + 0.3846153846 = 0.0000000000 0.0000000000 + -0.3076923077x + x2 = 0 + 0.3846153846 -0.3076923077x + x2 = 0 + 0.3846153846 Combine like terms: 0 + 0.3846153846 = 0.3846153846 -0.3076923077x + x2 = 0.3846153846 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 = 0.3846153846 + 0.02366863907 Reorder the terms: 0.02366863907 + -0.3076923077x + x2 = 0.3846153846 + 0.02366863907 Combine like terms: 0.3846153846 + 0.02366863907 = 0.40828402367 0.02366863907 + -0.3076923077x + x2 = 0.40828402367 Factor a perfect square on the left side: (x + -0.1538461539)(x + -0.1538461539) = 0.40828402367 Calculate the square root of the right side: 0.638971066 Break this problem into two subproblems by setting (x + -0.1538461539) equal to 0.638971066 and -0.638971066.Subproblem 1
x + -0.1538461539 = 0.638971066 Simplifying x + -0.1538461539 = 0.638971066 Reorder the terms: -0.1538461539 + x = 0.638971066 Solving -0.1538461539 + x = 0.638971066 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 = 0.638971066 + 0.1538461539 Combine like terms: -0.1538461539 + 0.1538461539 = 0.0000000000 0.0000000000 + x = 0.638971066 + 0.1538461539 x = 0.638971066 + 0.1538461539 Combine like terms: 0.638971066 + 0.1538461539 = 0.7928172199 x = 0.7928172199 Simplifying x = 0.7928172199Subproblem 2
x + -0.1538461539 = -0.638971066 Simplifying x + -0.1538461539 = -0.638971066 Reorder the terms: -0.1538461539 + x = -0.638971066 Solving -0.1538461539 + x = -0.638971066 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 = -0.638971066 + 0.1538461539 Combine like terms: -0.1538461539 + 0.1538461539 = 0.0000000000 0.0000000000 + x = -0.638971066 + 0.1538461539 x = -0.638971066 + 0.1538461539 Combine like terms: -0.638971066 + 0.1538461539 = -0.4851249121 x = -0.4851249121 Simplifying x = -0.4851249121Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7928172199, -0.4851249121}
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