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Simplifying (3x + -4)(x + 6) = x + 12 Reorder the terms: (-4 + 3x)(x + 6) = x + 12 Reorder the terms: (-4 + 3x)(6 + x) = x + 12 Multiply (-4 + 3x) * (6 + x) (-4(6 + x) + 3x * (6 + x)) = x + 12 ((6 * -4 + x * -4) + 3x * (6 + x)) = x + 12 ((-24 + -4x) + 3x * (6 + x)) = x + 12 (-24 + -4x + (6 * 3x + x * 3x)) = x + 12 (-24 + -4x + (18x + 3x2)) = x + 12 Combine like terms: -4x + 18x = 14x (-24 + 14x + 3x2) = x + 12 Reorder the terms: -24 + 14x + 3x2 = 12 + x Solving -24 + 14x + 3x2 = 12 + x Solving for variable 'x'. Reorder the terms: -24 + -12 + 14x + -1x + 3x2 = 12 + x + -12 + -1x Combine like terms: -24 + -12 = -36 -36 + 14x + -1x + 3x2 = 12 + x + -12 + -1x Combine like terms: 14x + -1x = 13x -36 + 13x + 3x2 = 12 + x + -12 + -1x Reorder the terms: -36 + 13x + 3x2 = 12 + -12 + x + -1x Combine like terms: 12 + -12 = 0 -36 + 13x + 3x2 = 0 + x + -1x -36 + 13x + 3x2 = x + -1x Combine like terms: x + -1x = 0 -36 + 13x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -12 + 4.333333333x + x2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + 4.333333333x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + 4.333333333x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 4.333333333x + x2 = 0 + 12 4.333333333x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 4.333333333x + x2 = 12 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 = 12 + 4.694444446 Reorder the terms: 4.694444446 + 4.333333333x + x2 = 12 + 4.694444446 Combine like terms: 12 + 4.694444446 = 16.694444446 4.694444446 + 4.333333333x + x2 = 16.694444446 Factor a perfect square on the left side: (x + 2.166666667)(x + 2.166666667) = 16.694444446 Calculate the square root of the right side: 4.085883558 Break this problem into two subproblems by setting (x + 2.166666667) equal to 4.085883558 and -4.085883558.Subproblem 1
x + 2.166666667 = 4.085883558 Simplifying x + 2.166666667 = 4.085883558 Reorder the terms: 2.166666667 + x = 4.085883558 Solving 2.166666667 + x = 4.085883558 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 = 4.085883558 + -2.166666667 Combine like terms: 2.166666667 + -2.166666667 = 0.000000000 0.000000000 + x = 4.085883558 + -2.166666667 x = 4.085883558 + -2.166666667 Combine like terms: 4.085883558 + -2.166666667 = 1.919216891 x = 1.919216891 Simplifying x = 1.919216891Subproblem 2
x + 2.166666667 = -4.085883558 Simplifying x + 2.166666667 = -4.085883558 Reorder the terms: 2.166666667 + x = -4.085883558 Solving 2.166666667 + x = -4.085883558 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 = -4.085883558 + -2.166666667 Combine like terms: 2.166666667 + -2.166666667 = 0.000000000 0.000000000 + x = -4.085883558 + -2.166666667 x = -4.085883558 + -2.166666667 Combine like terms: -4.085883558 + -2.166666667 = -6.252550225 x = -6.252550225 Simplifying x = -6.252550225Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.919216891, -6.252550225}
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