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Simplifying x = 3x + 13(x2 + 3) Reorder the terms: x = 3x + 13(3 + x2) x = 3x + (3 * 13 + x2 * 13) x = 3x + (39 + 13x2) Reorder the terms: x = 39 + 3x + 13x2 Solving x = 39 + 3x + 13x2 Solving for variable 'x'. Reorder the terms: -39 + x + -3x + -13x2 = 39 + 3x + 13x2 + -39 + -3x + -13x2 Combine like terms: x + -3x = -2x -39 + -2x + -13x2 = 39 + 3x + 13x2 + -39 + -3x + -13x2 Reorder the terms: -39 + -2x + -13x2 = 39 + -39 + 3x + -3x + 13x2 + -13x2 Combine like terms: 39 + -39 = 0 -39 + -2x + -13x2 = 0 + 3x + -3x + 13x2 + -13x2 -39 + -2x + -13x2 = 3x + -3x + 13x2 + -13x2 Combine like terms: 3x + -3x = 0 -39 + -2x + -13x2 = 0 + 13x2 + -13x2 -39 + -2x + -13x2 = 13x2 + -13x2 Combine like terms: 13x2 + -13x2 = 0 -39 + -2x + -13x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(39 + 2x + 13x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(39 + 2x + 13x2)' equal to zero and attempt to solve: Simplifying 39 + 2x + 13x2 = 0 Solving 39 + 2x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. 3 + 0.1538461538x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + 0.1538461538x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + 0.1538461538x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 0.1538461538x + x2 = 0 + -3 0.1538461538x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 0.1538461538x + x2 = -3 The x term is 0.1538461538x. Take half its coefficient (0.0769230769). Square it (0.005917159760) and add it to both sides. Add '0.005917159760' to each side of the equation. 0.1538461538x + 0.005917159760 + x2 = -3 + 0.005917159760 Reorder the terms: 0.005917159760 + 0.1538461538x + x2 = -3 + 0.005917159760 Combine like terms: -3 + 0.005917159760 = -2.99408284024 0.005917159760 + 0.1538461538x + x2 = -2.99408284024 Factor a perfect square on the left side: (x + 0.0769230769)(x + 0.0769230769) = -2.99408284024 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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