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Simplifying 3x(x + -5) + 4(3 + -2x) = 0 Reorder the terms: 3x(-5 + x) + 4(3 + -2x) = 0 (-5 * 3x + x * 3x) + 4(3 + -2x) = 0 (-15x + 3x2) + 4(3 + -2x) = 0 -15x + 3x2 + (3 * 4 + -2x * 4) = 0 -15x + 3x2 + (12 + -8x) = 0 Reorder the terms: 12 + -15x + -8x + 3x2 = 0 Combine like terms: -15x + -8x = -23x 12 + -23x + 3x2 = 0 Solving 12 + -23x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 4 + -7.666666667x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -7.666666667x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -7.666666667x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -7.666666667x + x2 = 0 + -4 -7.666666667x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -7.666666667x + x2 = -4 The x term is -7.666666667x. Take half its coefficient (-3.833333334). Square it (14.69444445) and add it to both sides. Add '14.69444445' to each side of the equation. -7.666666667x + 14.69444445 + x2 = -4 + 14.69444445 Reorder the terms: 14.69444445 + -7.666666667x + x2 = -4 + 14.69444445 Combine like terms: -4 + 14.69444445 = 10.69444445 14.69444445 + -7.666666667x + x2 = 10.69444445 Factor a perfect square on the left side: (x + -3.833333334)(x + -3.833333334) = 10.69444445 Calculate the square root of the right side: 3.270236146 Break this problem into two subproblems by setting (x + -3.833333334) equal to 3.270236146 and -3.270236146.Subproblem 1
x + -3.833333334 = 3.270236146 Simplifying x + -3.833333334 = 3.270236146 Reorder the terms: -3.833333334 + x = 3.270236146 Solving -3.833333334 + x = 3.270236146 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.833333334' to each side of the equation. -3.833333334 + 3.833333334 + x = 3.270236146 + 3.833333334 Combine like terms: -3.833333334 + 3.833333334 = 0.000000000 0.000000000 + x = 3.270236146 + 3.833333334 x = 3.270236146 + 3.833333334 Combine like terms: 3.270236146 + 3.833333334 = 7.10356948 x = 7.10356948 Simplifying x = 7.10356948Subproblem 2
x + -3.833333334 = -3.270236146 Simplifying x + -3.833333334 = -3.270236146 Reorder the terms: -3.833333334 + x = -3.270236146 Solving -3.833333334 + x = -3.270236146 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.833333334' to each side of the equation. -3.833333334 + 3.833333334 + x = -3.270236146 + 3.833333334 Combine like terms: -3.833333334 + 3.833333334 = 0.000000000 0.000000000 + x = -3.270236146 + 3.833333334 x = -3.270236146 + 3.833333334 Combine like terms: -3.270236146 + 3.833333334 = 0.563097188 x = 0.563097188 Simplifying x = 0.563097188Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.10356948, 0.563097188}
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