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Simplifying 3x(x + 5) + -6 = 2x + 16 Reorder the terms: 3x(5 + x) + -6 = 2x + 16 (5 * 3x + x * 3x) + -6 = 2x + 16 (15x + 3x2) + -6 = 2x + 16 Reorder the terms: -6 + 15x + 3x2 = 2x + 16 Reorder the terms: -6 + 15x + 3x2 = 16 + 2x Solving -6 + 15x + 3x2 = 16 + 2x Solving for variable 'x'. Reorder the terms: -6 + -16 + 15x + -2x + 3x2 = 16 + 2x + -16 + -2x Combine like terms: -6 + -16 = -22 -22 + 15x + -2x + 3x2 = 16 + 2x + -16 + -2x Combine like terms: 15x + -2x = 13x -22 + 13x + 3x2 = 16 + 2x + -16 + -2x Reorder the terms: -22 + 13x + 3x2 = 16 + -16 + 2x + -2x Combine like terms: 16 + -16 = 0 -22 + 13x + 3x2 = 0 + 2x + -2x -22 + 13x + 3x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -22 + 13x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -7.333333333 + 4.333333333x + x2 = 0 Move the constant term to the right: Add '7.333333333' to each side of the equation. -7.333333333 + 4.333333333x + 7.333333333 + x2 = 0 + 7.333333333 Reorder the terms: -7.333333333 + 7.333333333 + 4.333333333x + x2 = 0 + 7.333333333 Combine like terms: -7.333333333 + 7.333333333 = 0.000000000 0.000000000 + 4.333333333x + x2 = 0 + 7.333333333 4.333333333x + x2 = 0 + 7.333333333 Combine like terms: 0 + 7.333333333 = 7.333333333 4.333333333x + x2 = 7.333333333 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 = 7.333333333 + 4.694444446 Reorder the terms: 4.694444446 + 4.333333333x + x2 = 7.333333333 + 4.694444446 Combine like terms: 7.333333333 + 4.694444446 = 12.027777779 4.694444446 + 4.333333333x + x2 = 12.027777779 Factor a perfect square on the left side: (x + 2.166666667)(x + 2.166666667) = 12.027777779 Calculate the square root of the right side: 3.468108675 Break this problem into two subproblems by setting (x + 2.166666667) equal to 3.468108675 and -3.468108675.Subproblem 1
x + 2.166666667 = 3.468108675 Simplifying x + 2.166666667 = 3.468108675 Reorder the terms: 2.166666667 + x = 3.468108675 Solving 2.166666667 + x = 3.468108675 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 = 3.468108675 + -2.166666667 Combine like terms: 2.166666667 + -2.166666667 = 0.000000000 0.000000000 + x = 3.468108675 + -2.166666667 x = 3.468108675 + -2.166666667 Combine like terms: 3.468108675 + -2.166666667 = 1.301442008 x = 1.301442008 Simplifying x = 1.301442008Subproblem 2
x + 2.166666667 = -3.468108675 Simplifying x + 2.166666667 = -3.468108675 Reorder the terms: 2.166666667 + x = -3.468108675 Solving 2.166666667 + x = -3.468108675 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 = -3.468108675 + -2.166666667 Combine like terms: 2.166666667 + -2.166666667 = 0.000000000 0.000000000 + x = -3.468108675 + -2.166666667 x = -3.468108675 + -2.166666667 Combine like terms: -3.468108675 + -2.166666667 = -5.634775342 x = -5.634775342 Simplifying x = -5.634775342Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.301442008, -5.634775342}
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