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Simplifying 3x2 = 2(5x + -3x2 + 12) Reorder the terms: 3x2 = 2(12 + 5x + -3x2) 3x2 = (12 * 2 + 5x * 2 + -3x2 * 2) 3x2 = (24 + 10x + -6x2) Solving 3x2 = 24 + 10x + -6x2 Solving for variable 'x'. Reorder the terms: -24 + -10x + 3x2 + 6x2 = 24 + 10x + -6x2 + -24 + -10x + 6x2 Combine like terms: 3x2 + 6x2 = 9x2 -24 + -10x + 9x2 = 24 + 10x + -6x2 + -24 + -10x + 6x2 Reorder the terms: -24 + -10x + 9x2 = 24 + -24 + 10x + -10x + -6x2 + 6x2 Combine like terms: 24 + -24 = 0 -24 + -10x + 9x2 = 0 + 10x + -10x + -6x2 + 6x2 -24 + -10x + 9x2 = 10x + -10x + -6x2 + 6x2 Combine like terms: 10x + -10x = 0 -24 + -10x + 9x2 = 0 + -6x2 + 6x2 -24 + -10x + 9x2 = -6x2 + 6x2 Combine like terms: -6x2 + 6x2 = 0 -24 + -10x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -2.666666667 + -1.111111111x + x2 = 0 Move the constant term to the right: Add '2.666666667' to each side of the equation. -2.666666667 + -1.111111111x + 2.666666667 + x2 = 0 + 2.666666667 Reorder the terms: -2.666666667 + 2.666666667 + -1.111111111x + x2 = 0 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + -1.111111111x + x2 = 0 + 2.666666667 -1.111111111x + x2 = 0 + 2.666666667 Combine like terms: 0 + 2.666666667 = 2.666666667 -1.111111111x + x2 = 2.666666667 The x term is -1.111111111x. Take half its coefficient (-0.5555555555). Square it (0.3086419752) and add it to both sides. Add '0.3086419752' to each side of the equation. -1.111111111x + 0.3086419752 + x2 = 2.666666667 + 0.3086419752 Reorder the terms: 0.3086419752 + -1.111111111x + x2 = 2.666666667 + 0.3086419752 Combine like terms: 2.666666667 + 0.3086419752 = 2.9753086422 0.3086419752 + -1.111111111x + x2 = 2.9753086422 Factor a perfect square on the left side: (x + -0.5555555555)(x + -0.5555555555) = 2.9753086422 Calculate the square root of the right side: 1.7249083 Break this problem into two subproblems by setting (x + -0.5555555555) equal to 1.7249083 and -1.7249083.Subproblem 1
x + -0.5555555555 = 1.7249083 Simplifying x + -0.5555555555 = 1.7249083 Reorder the terms: -0.5555555555 + x = 1.7249083 Solving -0.5555555555 + x = 1.7249083 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5555555555' to each side of the equation. -0.5555555555 + 0.5555555555 + x = 1.7249083 + 0.5555555555 Combine like terms: -0.5555555555 + 0.5555555555 = 0.0000000000 0.0000000000 + x = 1.7249083 + 0.5555555555 x = 1.7249083 + 0.5555555555 Combine like terms: 1.7249083 + 0.5555555555 = 2.2804638555 x = 2.2804638555 Simplifying x = 2.2804638555Subproblem 2
x + -0.5555555555 = -1.7249083 Simplifying x + -0.5555555555 = -1.7249083 Reorder the terms: -0.5555555555 + x = -1.7249083 Solving -0.5555555555 + x = -1.7249083 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5555555555' to each side of the equation. -0.5555555555 + 0.5555555555 + x = -1.7249083 + 0.5555555555 Combine like terms: -0.5555555555 + 0.5555555555 = 0.0000000000 0.0000000000 + x = -1.7249083 + 0.5555555555 x = -1.7249083 + 0.5555555555 Combine like terms: -1.7249083 + 0.5555555555 = -1.1693527445 x = -1.1693527445 Simplifying x = -1.1693527445Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.2804638555, -1.1693527445}
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