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Simplifying 3x2 + 2x + -11 = 13 + 12x Reorder the terms: -11 + 2x + 3x2 = 13 + 12x Solving -11 + 2x + 3x2 = 13 + 12x Solving for variable 'x'. Reorder the terms: -11 + -13 + 2x + -12x + 3x2 = 13 + 12x + -13 + -12x Combine like terms: -11 + -13 = -24 -24 + 2x + -12x + 3x2 = 13 + 12x + -13 + -12x Combine like terms: 2x + -12x = -10x -24 + -10x + 3x2 = 13 + 12x + -13 + -12x Reorder the terms: -24 + -10x + 3x2 = 13 + -13 + 12x + -12x Combine like terms: 13 + -13 = 0 -24 + -10x + 3x2 = 0 + 12x + -12x -24 + -10x + 3x2 = 12x + -12x Combine like terms: 12x + -12x = 0 -24 + -10x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -8 + -3.333333333x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -3.333333333x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + -3.333333333x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -3.333333333x + x2 = 0 + 8 -3.333333333x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 -3.333333333x + x2 = 8 The x term is -3.333333333x. Take half its coefficient (-1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. -3.333333333x + 2.777777779 + x2 = 8 + 2.777777779 Reorder the terms: 2.777777779 + -3.333333333x + x2 = 8 + 2.777777779 Combine like terms: 8 + 2.777777779 = 10.777777779 2.777777779 + -3.333333333x + x2 = 10.777777779 Factor a perfect square on the left side: (x + -1.666666667)(x + -1.666666667) = 10.777777779 Calculate the square root of the right side: 3.282952601 Break this problem into two subproblems by setting (x + -1.666666667) equal to 3.282952601 and -3.282952601.Subproblem 1
x + -1.666666667 = 3.282952601 Simplifying x + -1.666666667 = 3.282952601 Reorder the terms: -1.666666667 + x = 3.282952601 Solving -1.666666667 + x = 3.282952601 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + x = 3.282952601 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = 3.282952601 + 1.666666667 x = 3.282952601 + 1.666666667 Combine like terms: 3.282952601 + 1.666666667 = 4.949619268 x = 4.949619268 Simplifying x = 4.949619268Subproblem 2
x + -1.666666667 = -3.282952601 Simplifying x + -1.666666667 = -3.282952601 Reorder the terms: -1.666666667 + x = -3.282952601 Solving -1.666666667 + x = -3.282952601 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + x = -3.282952601 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = -3.282952601 + 1.666666667 x = -3.282952601 + 1.666666667 Combine like terms: -3.282952601 + 1.666666667 = -1.616285934 x = -1.616285934 Simplifying x = -1.616285934Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.949619268, -1.616285934}
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