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Simplifying 3x * x = x + 12x + 3 Multiply x * x 3x2 = x + 12x + 3 Reorder the terms: 3x2 = 3 + x + 12x Combine like terms: x + 12x = 13x 3x2 = 3 + 13x Solving 3x2 = 3 + 13x Solving for variable 'x'. Reorder the terms: -3 + -13x + 3x2 = 3 + 13x + -3 + -13x Reorder the terms: -3 + -13x + 3x2 = 3 + -3 + 13x + -13x Combine like terms: 3 + -3 = 0 -3 + -13x + 3x2 = 0 + 13x + -13x -3 + -13x + 3x2 = 13x + -13x Combine like terms: 13x + -13x = 0 -3 + -13x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1 + -4.333333333x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -4.333333333x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -4.333333333x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4.333333333x + x2 = 0 + 1 -4.333333333x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -4.333333333x + x2 = 1 The x term is -4.333333333x. Take half its coefficient (-2.166666667). Square it (4.694444446) and add it to both sides. Add '4.694444446' to each side of the equation. -4.333333333x + 4.694444446 + x2 = 1 + 4.694444446 Reorder the terms: 4.694444446 + -4.333333333x + x2 = 1 + 4.694444446 Combine like terms: 1 + 4.694444446 = 5.694444446 4.694444446 + -4.333333333x + x2 = 5.694444446 Factor a perfect square on the left side: (x + -2.166666667)(x + -2.166666667) = 5.694444446 Calculate the square root of the right side: 2.386303511 Break this problem into two subproblems by setting (x + -2.166666667) equal to 2.386303511 and -2.386303511.Subproblem 1
x + -2.166666667 = 2.386303511 Simplifying x + -2.166666667 = 2.386303511 Reorder the terms: -2.166666667 + x = 2.386303511 Solving -2.166666667 + x = 2.386303511 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.166666667' to each side of the equation. -2.166666667 + 2.166666667 + x = 2.386303511 + 2.166666667 Combine like terms: -2.166666667 + 2.166666667 = 0.000000000 0.000000000 + x = 2.386303511 + 2.166666667 x = 2.386303511 + 2.166666667 Combine like terms: 2.386303511 + 2.166666667 = 4.552970178 x = 4.552970178 Simplifying x = 4.552970178Subproblem 2
x + -2.166666667 = -2.386303511 Simplifying x + -2.166666667 = -2.386303511 Reorder the terms: -2.166666667 + x = -2.386303511 Solving -2.166666667 + x = -2.386303511 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.166666667' to each side of the equation. -2.166666667 + 2.166666667 + x = -2.386303511 + 2.166666667 Combine like terms: -2.166666667 + 2.166666667 = 0.000000000 0.000000000 + x = -2.386303511 + 2.166666667 x = -2.386303511 + 2.166666667 Combine like terms: -2.386303511 + 2.166666667 = -0.219636844 x = -0.219636844 Simplifying x = -0.219636844Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.552970178, -0.219636844}
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