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Simplifying 3x(x + -4) = x + 6 Reorder the terms: 3x(-4 + x) = x + 6 (-4 * 3x + x * 3x) = x + 6 (-12x + 3x2) = x + 6 Reorder the terms: -12x + 3x2 = 6 + x Solving -12x + 3x2 = 6 + x Solving for variable 'x'. Reorder the terms: -6 + -12x + -1x + 3x2 = 6 + x + -6 + -1x Combine like terms: -12x + -1x = -13x -6 + -13x + 3x2 = 6 + x + -6 + -1x Reorder the terms: -6 + -13x + 3x2 = 6 + -6 + x + -1x Combine like terms: 6 + -6 = 0 -6 + -13x + 3x2 = 0 + x + -1x -6 + -13x + 3x2 = x + -1x Combine like terms: x + -1x = 0 -6 + -13x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2 + -4.333333333x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -4.333333333x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -4.333333333x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -4.333333333x + x2 = 0 + 2 -4.333333333x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -4.333333333x + x2 = 2 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 = 2 + 4.694444446 Reorder the terms: 4.694444446 + -4.333333333x + x2 = 2 + 4.694444446 Combine like terms: 2 + 4.694444446 = 6.694444446 4.694444446 + -4.333333333x + x2 = 6.694444446 Factor a perfect square on the left side: (x + -2.166666667)(x + -2.166666667) = 6.694444446 Calculate the square root of the right side: 2.58736245 Break this problem into two subproblems by setting (x + -2.166666667) equal to 2.58736245 and -2.58736245.Subproblem 1
x + -2.166666667 = 2.58736245 Simplifying x + -2.166666667 = 2.58736245 Reorder the terms: -2.166666667 + x = 2.58736245 Solving -2.166666667 + x = 2.58736245 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 = 2.58736245 + 2.166666667 Combine like terms: -2.166666667 + 2.166666667 = 0.000000000 0.000000000 + x = 2.58736245 + 2.166666667 x = 2.58736245 + 2.166666667 Combine like terms: 2.58736245 + 2.166666667 = 4.754029117 x = 4.754029117 Simplifying x = 4.754029117Subproblem 2
x + -2.166666667 = -2.58736245 Simplifying x + -2.166666667 = -2.58736245 Reorder the terms: -2.166666667 + x = -2.58736245 Solving -2.166666667 + x = -2.58736245 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 = -2.58736245 + 2.166666667 Combine like terms: -2.166666667 + 2.166666667 = 0.000000000 0.000000000 + x = -2.58736245 + 2.166666667 x = -2.58736245 + 2.166666667 Combine like terms: -2.58736245 + 2.166666667 = -0.420695783 x = -0.420695783 Simplifying x = -0.420695783Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.754029117, -0.420695783}
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