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Simplifying 4x + x + (3 + 2x) = 3x(x + -2) Remove parenthesis around (3 + 2x) 4x + x + 3 + 2x = 3x(x + -2) Reorder the terms: 3 + 4x + x + 2x = 3x(x + -2) Combine like terms: 4x + x = 5x 3 + 5x + 2x = 3x(x + -2) Combine like terms: 5x + 2x = 7x 3 + 7x = 3x(x + -2) Reorder the terms: 3 + 7x = 3x(-2 + x) 3 + 7x = (-2 * 3x + x * 3x) 3 + 7x = (-6x + 3x2) Solving 3 + 7x = -6x + 3x2 Solving for variable 'x'. Combine like terms: 7x + 6x = 13x 3 + 13x + -3x2 = -6x + 3x2 + 6x + -3x2 Reorder the terms: 3 + 13x + -3x2 = -6x + 6x + 3x2 + -3x2 Combine like terms: -6x + 6x = 0 3 + 13x + -3x2 = 0 + 3x2 + -3x2 3 + 13x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 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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