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Simplifying 6 + -3x(1 + -1x) = 42 + -67x 6 + (1 * -3x + -1x * -3x) = 42 + -67x 6 + (-3x + 3x2) = 42 + -67x Solving 6 + -3x + 3x2 = 42 + -67x Solving for variable 'x'. Reorder the terms: 6 + -42 + -3x + 67x + 3x2 = 42 + -67x + -42 + 67x Combine like terms: 6 + -42 = -36 -36 + -3x + 67x + 3x2 = 42 + -67x + -42 + 67x Combine like terms: -3x + 67x = 64x -36 + 64x + 3x2 = 42 + -67x + -42 + 67x Reorder the terms: -36 + 64x + 3x2 = 42 + -42 + -67x + 67x Combine like terms: 42 + -42 = 0 -36 + 64x + 3x2 = 0 + -67x + 67x -36 + 64x + 3x2 = -67x + 67x Combine like terms: -67x + 67x = 0 -36 + 64x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -12 + 21.33333333x + x2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + 21.33333333x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + 21.33333333x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 21.33333333x + x2 = 0 + 12 21.33333333x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 21.33333333x + x2 = 12 The x term is 21.33333333x. Take half its coefficient (10.66666667). Square it (113.7777778) and add it to both sides. Add '113.7777778' to each side of the equation. 21.33333333x + 113.7777778 + x2 = 12 + 113.7777778 Reorder the terms: 113.7777778 + 21.33333333x + x2 = 12 + 113.7777778 Combine like terms: 12 + 113.7777778 = 125.7777778 113.7777778 + 21.33333333x + x2 = 125.7777778 Factor a perfect square on the left side: (x + 10.66666667)(x + 10.66666667) = 125.7777778 Calculate the square root of the right side: 11.215069228 Break this problem into two subproblems by setting (x + 10.66666667) equal to 11.215069228 and -11.215069228.Subproblem 1
x + 10.66666667 = 11.215069228 Simplifying x + 10.66666667 = 11.215069228 Reorder the terms: 10.66666667 + x = 11.215069228 Solving 10.66666667 + x = 11.215069228 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.66666667' to each side of the equation. 10.66666667 + -10.66666667 + x = 11.215069228 + -10.66666667 Combine like terms: 10.66666667 + -10.66666667 = 0.00000000 0.00000000 + x = 11.215069228 + -10.66666667 x = 11.215069228 + -10.66666667 Combine like terms: 11.215069228 + -10.66666667 = 0.548402558 x = 0.548402558 Simplifying x = 0.548402558Subproblem 2
x + 10.66666667 = -11.215069228 Simplifying x + 10.66666667 = -11.215069228 Reorder the terms: 10.66666667 + x = -11.215069228 Solving 10.66666667 + x = -11.215069228 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.66666667' to each side of the equation. 10.66666667 + -10.66666667 + x = -11.215069228 + -10.66666667 Combine like terms: 10.66666667 + -10.66666667 = 0.00000000 0.00000000 + x = -11.215069228 + -10.66666667 x = -11.215069228 + -10.66666667 Combine like terms: -11.215069228 + -10.66666667 = -21.881735898 x = -21.881735898 Simplifying x = -21.881735898Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.548402558, -21.881735898}
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