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Simplifying 3 + 2x = -3x(x + -5) Reorder the terms: 3 + 2x = -3x(-5 + x) 3 + 2x = (-5 * -3x + x * -3x) 3 + 2x = (15x + -3x2) Solving 3 + 2x = 15x + -3x2 Solving for variable 'x'. Combine like terms: 2x + -15x = -13x 3 + -13x + 3x2 = 15x + -3x2 + -15x + 3x2 Reorder the terms: 3 + -13x + 3x2 = 15x + -15x + -3x2 + 3x2 Combine like terms: 15x + -15x = 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 = 3.694444446 4.694444446 + -4.333333333x + x2 = 3.694444446 Factor a perfect square on the left side: (x + -2.166666667)(x + -2.166666667) = 3.694444446 Calculate the square root of the right side: 1.922093766 Break this problem into two subproblems by setting (x + -2.166666667) equal to 1.922093766 and -1.922093766.Subproblem 1
x + -2.166666667 = 1.922093766 Simplifying x + -2.166666667 = 1.922093766 Reorder the terms: -2.166666667 + x = 1.922093766 Solving -2.166666667 + x = 1.922093766 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 = 1.922093766 + 2.166666667 Combine like terms: -2.166666667 + 2.166666667 = 0.000000000 0.000000000 + x = 1.922093766 + 2.166666667 x = 1.922093766 + 2.166666667 Combine like terms: 1.922093766 + 2.166666667 = 4.088760433 x = 4.088760433 Simplifying x = 4.088760433Subproblem 2
x + -2.166666667 = -1.922093766 Simplifying x + -2.166666667 = -1.922093766 Reorder the terms: -2.166666667 + x = -1.922093766 Solving -2.166666667 + x = -1.922093766 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 = -1.922093766 + 2.166666667 Combine like terms: -2.166666667 + 2.166666667 = 0.000000000 0.000000000 + x = -1.922093766 + 2.166666667 x = -1.922093766 + 2.166666667 Combine like terms: -1.922093766 + 2.166666667 = 0.244572901 x = 0.244572901 Simplifying x = 0.244572901Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.088760433, 0.244572901}
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