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Simplifying 9x2 + 3x + -13 = 0 Reorder the terms: -13 + 3x + 9x2 = 0 Solving -13 + 3x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.444444444 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '1.444444444' to each side of the equation. -1.444444444 + 0.3333333333x + 1.444444444 + x2 = 0 + 1.444444444 Reorder the terms: -1.444444444 + 1.444444444 + 0.3333333333x + x2 = 0 + 1.444444444 Combine like terms: -1.444444444 + 1.444444444 = 0.000000000 0.000000000 + 0.3333333333x + x2 = 0 + 1.444444444 0.3333333333x + x2 = 0 + 1.444444444 Combine like terms: 0 + 1.444444444 = 1.444444444 0.3333333333x + x2 = 1.444444444 The x term is 0.3333333333x. Take half its coefficient (0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. 0.3333333333x + 0.02777777779 + x2 = 1.444444444 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333x + x2 = 1.444444444 + 0.02777777779 Combine like terms: 1.444444444 + 0.02777777779 = 1.47222222179 0.02777777779 + 0.3333333333x + x2 = 1.47222222179 Factor a perfect square on the left side: (x + 0.1666666667)(x + 0.1666666667) = 1.47222222179 Calculate the square root of the right side: 1.213351648 Break this problem into two subproblems by setting (x + 0.1666666667) equal to 1.213351648 and -1.213351648.Subproblem 1
x + 0.1666666667 = 1.213351648 Simplifying x + 0.1666666667 = 1.213351648 Reorder the terms: 0.1666666667 + x = 1.213351648 Solving 0.1666666667 + x = 1.213351648 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = 1.213351648 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = 1.213351648 + -0.1666666667 x = 1.213351648 + -0.1666666667 Combine like terms: 1.213351648 + -0.1666666667 = 1.0466849813 x = 1.0466849813 Simplifying x = 1.0466849813Subproblem 2
x + 0.1666666667 = -1.213351648 Simplifying x + 0.1666666667 = -1.213351648 Reorder the terms: 0.1666666667 + x = -1.213351648 Solving 0.1666666667 + x = -1.213351648 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = -1.213351648 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = -1.213351648 + -0.1666666667 x = -1.213351648 + -0.1666666667 Combine like terms: -1.213351648 + -0.1666666667 = -1.3800183147 x = -1.3800183147 Simplifying x = -1.3800183147Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0466849813, -1.3800183147}
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