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Simplifying 3x(x + -6) = x + 9 Reorder the terms: 3x(-6 + x) = x + 9 (-6 * 3x + x * 3x) = x + 9 (-18x + 3x2) = x + 9 Reorder the terms: -18x + 3x2 = 9 + x Solving -18x + 3x2 = 9 + x Solving for variable 'x'. Reorder the terms: -9 + -18x + -1x + 3x2 = 9 + x + -9 + -1x Combine like terms: -18x + -1x = -19x -9 + -19x + 3x2 = 9 + x + -9 + -1x Reorder the terms: -9 + -19x + 3x2 = 9 + -9 + x + -1x Combine like terms: 9 + -9 = 0 -9 + -19x + 3x2 = 0 + x + -1x -9 + -19x + 3x2 = x + -1x Combine like terms: x + -1x = 0 -9 + -19x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3 + -6.333333333x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -6.333333333x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -6.333333333x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -6.333333333x + x2 = 0 + 3 -6.333333333x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -6.333333333x + x2 = 3 The x term is -6.333333333x. Take half its coefficient (-3.166666667). Square it (10.02777778) and add it to both sides. Add '10.02777778' to each side of the equation. -6.333333333x + 10.02777778 + x2 = 3 + 10.02777778 Reorder the terms: 10.02777778 + -6.333333333x + x2 = 3 + 10.02777778 Combine like terms: 3 + 10.02777778 = 13.02777778 10.02777778 + -6.333333333x + x2 = 13.02777778 Factor a perfect square on the left side: (x + -3.166666667)(x + -3.166666667) = 13.02777778 Calculate the square root of the right side: 3.609401305 Break this problem into two subproblems by setting (x + -3.166666667) equal to 3.609401305 and -3.609401305.Subproblem 1
x + -3.166666667 = 3.609401305 Simplifying x + -3.166666667 = 3.609401305 Reorder the terms: -3.166666667 + x = 3.609401305 Solving -3.166666667 + x = 3.609401305 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.166666667' to each side of the equation. -3.166666667 + 3.166666667 + x = 3.609401305 + 3.166666667 Combine like terms: -3.166666667 + 3.166666667 = 0.000000000 0.000000000 + x = 3.609401305 + 3.166666667 x = 3.609401305 + 3.166666667 Combine like terms: 3.609401305 + 3.166666667 = 6.776067972 x = 6.776067972 Simplifying x = 6.776067972Subproblem 2
x + -3.166666667 = -3.609401305 Simplifying x + -3.166666667 = -3.609401305 Reorder the terms: -3.166666667 + x = -3.609401305 Solving -3.166666667 + x = -3.609401305 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.166666667' to each side of the equation. -3.166666667 + 3.166666667 + x = -3.609401305 + 3.166666667 Combine like terms: -3.166666667 + 3.166666667 = 0.000000000 0.000000000 + x = -3.609401305 + 3.166666667 x = -3.609401305 + 3.166666667 Combine like terms: -3.609401305 + 3.166666667 = -0.442734638 x = -0.442734638 Simplifying x = -0.442734638Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.776067972, -0.442734638}
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