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Simplifying 13x2 + -3x + -5 = 0 Reorder the terms: -5 + -3x + 13x2 = 0 Solving -5 + -3x + 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'. -0.3846153846 + -0.2307692308x + x2 = 0 Move the constant term to the right: Add '0.3846153846' to each side of the equation. -0.3846153846 + -0.2307692308x + 0.3846153846 + x2 = 0 + 0.3846153846 Reorder the terms: -0.3846153846 + 0.3846153846 + -0.2307692308x + x2 = 0 + 0.3846153846 Combine like terms: -0.3846153846 + 0.3846153846 = 0.0000000000 0.0000000000 + -0.2307692308x + x2 = 0 + 0.3846153846 -0.2307692308x + x2 = 0 + 0.3846153846 Combine like terms: 0 + 0.3846153846 = 0.3846153846 -0.2307692308x + x2 = 0.3846153846 The x term is -0.2307692308x. Take half its coefficient (-0.1153846154). Square it (0.01331360947) and add it to both sides. Add '0.01331360947' to each side of the equation. -0.2307692308x + 0.01331360947 + x2 = 0.3846153846 + 0.01331360947 Reorder the terms: 0.01331360947 + -0.2307692308x + x2 = 0.3846153846 + 0.01331360947 Combine like terms: 0.3846153846 + 0.01331360947 = 0.39792899407 0.01331360947 + -0.2307692308x + x2 = 0.39792899407 Factor a perfect square on the left side: (x + -0.1153846154)(x + -0.1153846154) = 0.39792899407 Calculate the square root of the right side: 0.630816133 Break this problem into two subproblems by setting (x + -0.1153846154) equal to 0.630816133 and -0.630816133.Subproblem 1
x + -0.1153846154 = 0.630816133 Simplifying x + -0.1153846154 = 0.630816133 Reorder the terms: -0.1153846154 + x = 0.630816133 Solving -0.1153846154 + x = 0.630816133 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1153846154' to each side of the equation. -0.1153846154 + 0.1153846154 + x = 0.630816133 + 0.1153846154 Combine like terms: -0.1153846154 + 0.1153846154 = 0.0000000000 0.0000000000 + x = 0.630816133 + 0.1153846154 x = 0.630816133 + 0.1153846154 Combine like terms: 0.630816133 + 0.1153846154 = 0.7462007484 x = 0.7462007484 Simplifying x = 0.7462007484Subproblem 2
x + -0.1153846154 = -0.630816133 Simplifying x + -0.1153846154 = -0.630816133 Reorder the terms: -0.1153846154 + x = -0.630816133 Solving -0.1153846154 + x = -0.630816133 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1153846154' to each side of the equation. -0.1153846154 + 0.1153846154 + x = -0.630816133 + 0.1153846154 Combine like terms: -0.1153846154 + 0.1153846154 = 0.0000000000 0.0000000000 + x = -0.630816133 + 0.1153846154 x = -0.630816133 + 0.1153846154 Combine like terms: -0.630816133 + 0.1153846154 = -0.5154315176 x = -0.5154315176 Simplifying x = -0.5154315176Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7462007484, -0.5154315176}
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