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Simplifying -1x2 + 30 + 4x = 2x2 + 14x + 6 Reorder the terms: 30 + 4x + -1x2 = 2x2 + 14x + 6 Reorder the terms: 30 + 4x + -1x2 = 6 + 14x + 2x2 Solving 30 + 4x + -1x2 = 6 + 14x + 2x2 Solving for variable 'x'. Reorder the terms: 30 + -6 + 4x + -14x + -1x2 + -2x2 = 6 + 14x + 2x2 + -6 + -14x + -2x2 Combine like terms: 30 + -6 = 24 24 + 4x + -14x + -1x2 + -2x2 = 6 + 14x + 2x2 + -6 + -14x + -2x2 Combine like terms: 4x + -14x = -10x 24 + -10x + -1x2 + -2x2 = 6 + 14x + 2x2 + -6 + -14x + -2x2 Combine like terms: -1x2 + -2x2 = -3x2 24 + -10x + -3x2 = 6 + 14x + 2x2 + -6 + -14x + -2x2 Reorder the terms: 24 + -10x + -3x2 = 6 + -6 + 14x + -14x + 2x2 + -2x2 Combine like terms: 6 + -6 = 0 24 + -10x + -3x2 = 0 + 14x + -14x + 2x2 + -2x2 24 + -10x + -3x2 = 14x + -14x + 2x2 + -2x2 Combine like terms: 14x + -14x = 0 24 + -10x + -3x2 = 0 + 2x2 + -2x2 24 + -10x + -3x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 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 = 1.616285934 x = 1.616285934 Simplifying x = 1.616285934Subproblem 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 = -4.949619268 x = -4.949619268 Simplifying x = -4.949619268Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.616285934, -4.949619268}
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