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Simplifying 3x2 + 2x = -8x + 15 Reorder the terms: 2x + 3x2 = -8x + 15 Reorder the terms: 2x + 3x2 = 15 + -8x Solving 2x + 3x2 = 15 + -8x Solving for variable 'x'. Reorder the terms: -15 + 2x + 8x + 3x2 = 15 + -8x + -15 + 8x Combine like terms: 2x + 8x = 10x -15 + 10x + 3x2 = 15 + -8x + -15 + 8x Reorder the terms: -15 + 10x + 3x2 = 15 + -15 + -8x + 8x Combine like terms: 15 + -15 = 0 -15 + 10x + 3x2 = 0 + -8x + 8x -15 + 10x + 3x2 = -8x + 8x Combine like terms: -8x + 8x = 0 -15 + 10x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -5 + 3.333333333x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 3.333333333x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + 3.333333333x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 3.333333333x + x2 = 0 + 5 3.333333333x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 3.333333333x + x2 = 5 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 = 5 + 2.777777779 Reorder the terms: 2.777777779 + 3.333333333x + x2 = 5 + 2.777777779 Combine like terms: 5 + 2.777777779 = 7.777777779 2.777777779 + 3.333333333x + x2 = 7.777777779 Factor a perfect square on the left side: (x + 1.666666667)(x + 1.666666667) = 7.777777779 Calculate the square root of the right side: 2.788866755 Break this problem into two subproblems by setting (x + 1.666666667) equal to 2.788866755 and -2.788866755.Subproblem 1
x + 1.666666667 = 2.788866755 Simplifying x + 1.666666667 = 2.788866755 Reorder the terms: 1.666666667 + x = 2.788866755 Solving 1.666666667 + x = 2.788866755 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 = 2.788866755 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = 2.788866755 + -1.666666667 x = 2.788866755 + -1.666666667 Combine like terms: 2.788866755 + -1.666666667 = 1.122200088 x = 1.122200088 Simplifying x = 1.122200088Subproblem 2
x + 1.666666667 = -2.788866755 Simplifying x + 1.666666667 = -2.788866755 Reorder the terms: 1.666666667 + x = -2.788866755 Solving 1.666666667 + x = -2.788866755 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 = -2.788866755 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = -2.788866755 + -1.666666667 x = -2.788866755 + -1.666666667 Combine like terms: -2.788866755 + -1.666666667 = -4.455533422 x = -4.455533422 Simplifying x = -4.455533422Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.122200088, -4.455533422}
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