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Simplifying 3x2 + -2x + -39 = 0 Reorder the terms: -39 + -2x + 3x2 = 0 Solving -39 + -2x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -13 + -0.6666666667x + x2 = 0 Move the constant term to the right: Add '13' to each side of the equation. -13 + -0.6666666667x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + -0.6666666667x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -0.6666666667x + x2 = 0 + 13 -0.6666666667x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 -0.6666666667x + x2 = 13 The x term is -0.6666666667x. Take half its coefficient (-0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. -0.6666666667x + 0.1111111112 + x2 = 13 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667x + x2 = 13 + 0.1111111112 Combine like terms: 13 + 0.1111111112 = 13.1111111112 0.1111111112 + -0.6666666667x + x2 = 13.1111111112 Factor a perfect square on the left side: (x + -0.3333333334)(x + -0.3333333334) = 13.1111111112 Calculate the square root of the right side: 3.62092683 Break this problem into two subproblems by setting (x + -0.3333333334) equal to 3.62092683 and -3.62092683.Subproblem 1
x + -0.3333333334 = 3.62092683 Simplifying x + -0.3333333334 = 3.62092683 Reorder the terms: -0.3333333334 + x = 3.62092683 Solving -0.3333333334 + x = 3.62092683 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x = 3.62092683 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = 3.62092683 + 0.3333333334 x = 3.62092683 + 0.3333333334 Combine like terms: 3.62092683 + 0.3333333334 = 3.9542601634 x = 3.9542601634 Simplifying x = 3.9542601634Subproblem 2
x + -0.3333333334 = -3.62092683 Simplifying x + -0.3333333334 = -3.62092683 Reorder the terms: -0.3333333334 + x = -3.62092683 Solving -0.3333333334 + x = -3.62092683 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x = -3.62092683 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = -3.62092683 + 0.3333333334 x = -3.62092683 + 0.3333333334 Combine like terms: -3.62092683 + 0.3333333334 = -3.2875934966 x = -3.2875934966 Simplifying x = -3.2875934966Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.9542601634, -3.2875934966}
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