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Simplifying 3x(x + 4) = 2(5 + -1x) Reorder the terms: 3x(4 + x) = 2(5 + -1x) (4 * 3x + x * 3x) = 2(5 + -1x) (12x + 3x2) = 2(5 + -1x) 12x + 3x2 = (5 * 2 + -1x * 2) 12x + 3x2 = (10 + -2x) Solving 12x + 3x2 = 10 + -2x Solving for variable 'x'. Reorder the terms: -10 + 12x + 2x + 3x2 = 10 + -2x + -10 + 2x Combine like terms: 12x + 2x = 14x -10 + 14x + 3x2 = 10 + -2x + -10 + 2x Reorder the terms: -10 + 14x + 3x2 = 10 + -10 + -2x + 2x Combine like terms: 10 + -10 = 0 -10 + 14x + 3x2 = 0 + -2x + 2x -10 + 14x + 3x2 = -2x + 2x Combine like terms: -2x + 2x = 0 -10 + 14x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3.333333333 + 4.666666667x + x2 = 0 Move the constant term to the right: Add '3.333333333' to each side of the equation. -3.333333333 + 4.666666667x + 3.333333333 + x2 = 0 + 3.333333333 Reorder the terms: -3.333333333 + 3.333333333 + 4.666666667x + x2 = 0 + 3.333333333 Combine like terms: -3.333333333 + 3.333333333 = 0.000000000 0.000000000 + 4.666666667x + x2 = 0 + 3.333333333 4.666666667x + x2 = 0 + 3.333333333 Combine like terms: 0 + 3.333333333 = 3.333333333 4.666666667x + x2 = 3.333333333 The x term is 4.666666667x. Take half its coefficient (2.333333334). Square it (5.444444448) and add it to both sides. Add '5.444444448' to each side of the equation. 4.666666667x + 5.444444448 + x2 = 3.333333333 + 5.444444448 Reorder the terms: 5.444444448 + 4.666666667x + x2 = 3.333333333 + 5.444444448 Combine like terms: 3.333333333 + 5.444444448 = 8.777777781 5.444444448 + 4.666666667x + x2 = 8.777777781 Factor a perfect square on the left side: (x + 2.333333334)(x + 2.333333334) = 8.777777781 Calculate the square root of the right side: 2.962731473 Break this problem into two subproblems by setting (x + 2.333333334) equal to 2.962731473 and -2.962731473.Subproblem 1
x + 2.333333334 = 2.962731473 Simplifying x + 2.333333334 = 2.962731473 Reorder the terms: 2.333333334 + x = 2.962731473 Solving 2.333333334 + x = 2.962731473 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.333333334' to each side of the equation. 2.333333334 + -2.333333334 + x = 2.962731473 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + x = 2.962731473 + -2.333333334 x = 2.962731473 + -2.333333334 Combine like terms: 2.962731473 + -2.333333334 = 0.629398139 x = 0.629398139 Simplifying x = 0.629398139Subproblem 2
x + 2.333333334 = -2.962731473 Simplifying x + 2.333333334 = -2.962731473 Reorder the terms: 2.333333334 + x = -2.962731473 Solving 2.333333334 + x = -2.962731473 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.333333334' to each side of the equation. 2.333333334 + -2.333333334 + x = -2.962731473 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + x = -2.962731473 + -2.333333334 x = -2.962731473 + -2.333333334 Combine like terms: -2.962731473 + -2.333333334 = -5.296064807 x = -5.296064807 Simplifying x = -5.296064807Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.629398139, -5.296064807}
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