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Simplifying 3x(x + 4) + -6 = 5x + 5 + 5 Reorder the terms: 3x(4 + x) + -6 = 5x + 5 + 5 (4 * 3x + x * 3x) + -6 = 5x + 5 + 5 (12x + 3x2) + -6 = 5x + 5 + 5 Reorder the terms: -6 + 12x + 3x2 = 5x + 5 + 5 Reorder the terms: -6 + 12x + 3x2 = 5 + 5 + 5x Combine like terms: 5 + 5 = 10 -6 + 12x + 3x2 = 10 + 5x Solving -6 + 12x + 3x2 = 10 + 5x Solving for variable 'x'. Reorder the terms: -6 + -10 + 12x + -5x + 3x2 = 10 + 5x + -10 + -5x Combine like terms: -6 + -10 = -16 -16 + 12x + -5x + 3x2 = 10 + 5x + -10 + -5x Combine like terms: 12x + -5x = 7x -16 + 7x + 3x2 = 10 + 5x + -10 + -5x Reorder the terms: -16 + 7x + 3x2 = 10 + -10 + 5x + -5x Combine like terms: 10 + -10 = 0 -16 + 7x + 3x2 = 0 + 5x + -5x -16 + 7x + 3x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -16 + 7x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -5.333333333 + 2.333333333x + x2 = 0 Move the constant term to the right: Add '5.333333333' to each side of the equation. -5.333333333 + 2.333333333x + 5.333333333 + x2 = 0 + 5.333333333 Reorder the terms: -5.333333333 + 5.333333333 + 2.333333333x + x2 = 0 + 5.333333333 Combine like terms: -5.333333333 + 5.333333333 = 0.000000000 0.000000000 + 2.333333333x + x2 = 0 + 5.333333333 2.333333333x + x2 = 0 + 5.333333333 Combine like terms: 0 + 5.333333333 = 5.333333333 2.333333333x + x2 = 5.333333333 The x term is 2.333333333x. Take half its coefficient (1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. 2.333333333x + 1.361111112 + x2 = 5.333333333 + 1.361111112 Reorder the terms: 1.361111112 + 2.333333333x + x2 = 5.333333333 + 1.361111112 Combine like terms: 5.333333333 + 1.361111112 = 6.694444445 1.361111112 + 2.333333333x + x2 = 6.694444445 Factor a perfect square on the left side: (x + 1.166666667)(x + 1.166666667) = 6.694444445 Calculate the square root of the right side: 2.587362449 Break this problem into two subproblems by setting (x + 1.166666667) equal to 2.587362449 and -2.587362449.Subproblem 1
x + 1.166666667 = 2.587362449 Simplifying x + 1.166666667 = 2.587362449 Reorder the terms: 1.166666667 + x = 2.587362449 Solving 1.166666667 + x = 2.587362449 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = 2.587362449 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = 2.587362449 + -1.166666667 x = 2.587362449 + -1.166666667 Combine like terms: 2.587362449 + -1.166666667 = 1.420695782 x = 1.420695782 Simplifying x = 1.420695782Subproblem 2
x + 1.166666667 = -2.587362449 Simplifying x + 1.166666667 = -2.587362449 Reorder the terms: 1.166666667 + x = -2.587362449 Solving 1.166666667 + x = -2.587362449 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = -2.587362449 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = -2.587362449 + -1.166666667 x = -2.587362449 + -1.166666667 Combine like terms: -2.587362449 + -1.166666667 = -3.754029116 x = -3.754029116 Simplifying x = -3.754029116Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.420695782, -3.754029116}
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