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Simplifying 3x(2x + -1) = 2x + 13 Reorder the terms: 3x(-1 + 2x) = 2x + 13 (-1 * 3x + 2x * 3x) = 2x + 13 (-3x + 6x2) = 2x + 13 Reorder the terms: -3x + 6x2 = 13 + 2x Solving -3x + 6x2 = 13 + 2x Solving for variable 'x'. Reorder the terms: -13 + -3x + -2x + 6x2 = 13 + 2x + -13 + -2x Combine like terms: -3x + -2x = -5x -13 + -5x + 6x2 = 13 + 2x + -13 + -2x Reorder the terms: -13 + -5x + 6x2 = 13 + -13 + 2x + -2x Combine like terms: 13 + -13 = 0 -13 + -5x + 6x2 = 0 + 2x + -2x -13 + -5x + 6x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -13 + -5x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -2.166666667 + -0.8333333333x + x2 = 0 Move the constant term to the right: Add '2.166666667' to each side of the equation. -2.166666667 + -0.8333333333x + 2.166666667 + x2 = 0 + 2.166666667 Reorder the terms: -2.166666667 + 2.166666667 + -0.8333333333x + x2 = 0 + 2.166666667 Combine like terms: -2.166666667 + 2.166666667 = 0.000000000 0.000000000 + -0.8333333333x + x2 = 0 + 2.166666667 -0.8333333333x + x2 = 0 + 2.166666667 Combine like terms: 0 + 2.166666667 = 2.166666667 -0.8333333333x + x2 = 2.166666667 The x term is -0.8333333333x. Take half its coefficient (-0.4166666667). Square it (0.1736111111) and add it to both sides. Add '0.1736111111' to each side of the equation. -0.8333333333x + 0.1736111111 + x2 = 2.166666667 + 0.1736111111 Reorder the terms: 0.1736111111 + -0.8333333333x + x2 = 2.166666667 + 0.1736111111 Combine like terms: 2.166666667 + 0.1736111111 = 2.3402777781 0.1736111111 + -0.8333333333x + x2 = 2.3402777781 Factor a perfect square on the left side: (x + -0.4166666667)(x + -0.4166666667) = 2.3402777781 Calculate the square root of the right side: 1.529796646 Break this problem into two subproblems by setting (x + -0.4166666667) equal to 1.529796646 and -1.529796646.Subproblem 1
x + -0.4166666667 = 1.529796646 Simplifying x + -0.4166666667 = 1.529796646 Reorder the terms: -0.4166666667 + x = 1.529796646 Solving -0.4166666667 + x = 1.529796646 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4166666667' to each side of the equation. -0.4166666667 + 0.4166666667 + x = 1.529796646 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + x = 1.529796646 + 0.4166666667 x = 1.529796646 + 0.4166666667 Combine like terms: 1.529796646 + 0.4166666667 = 1.9464633127 x = 1.9464633127 Simplifying x = 1.9464633127Subproblem 2
x + -0.4166666667 = -1.529796646 Simplifying x + -0.4166666667 = -1.529796646 Reorder the terms: -0.4166666667 + x = -1.529796646 Solving -0.4166666667 + x = -1.529796646 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4166666667' to each side of the equation. -0.4166666667 + 0.4166666667 + x = -1.529796646 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + x = -1.529796646 + 0.4166666667 x = -1.529796646 + 0.4166666667 Combine like terms: -1.529796646 + 0.4166666667 = -1.1131299793 x = -1.1131299793 Simplifying x = -1.1131299793Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.9464633127, -1.1131299793}
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